The percentage of refrigerators that have lives between 11 years and 18 years is approximately 83.01%.
The values of 11 years and 18 years using the given mean and standard deviation, and then find the area under the standard normal curve between those two standardized values.
First, we standardize the value of 11 years:
z1 = (11 - 14) / 2.5 = -1.2
Next, we standardize the value of 18 years:
z2 = (18 - 14) / 2.5 = 1.6
Now we need to find the area under the standard normal curve between these two standardized values.
We can use a standard normal table or calculator to find this area.
Using a standard normal table, we can find the area between z = -1.2 and z = 1.6 by finding the area to the left of z = 1.6 and subtracting the area to the left of z = -1.2:
Area = P(-1.2 < z < 1.6) = P(z < 1.6) - P(z < -1.2)
Looking up these values in the standard normal table, we find:
P(z < 1.6) = 0.9452
P(z < -1.2) = 0.1151
Substituting these values, we get:
Area = 0.9452 - 0.1151 = 0.8301
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Two sisters purchased a car for 17698 if they each paid half how much money did they each pay
Answer: $8,849
Step-by-step explanation: 17,698 divided by two people is 8,849, therefore each sister paid $8,849.
Answer: $8849
Step-by-step explanation: We are given that the total amount both sisters pay is $17698. They each pay for a fraction though. That fraction is 1/2 since they each pay for half. We multiply this fraction by the total which is 17698 to find our answer.
If there were three sisters and they each paid one-third, we would multiply the total price by 1/3 to find our answer.
Dan is mailing packages. Each small package costs him $2.30 to send. Each large package costs him $3.90. How much will it cost him to send 4 small packages and 6 large packages?
Answer: $32.60
Step-by-step explanation:
(4)(2.30) + (6)(3.90)
= 32.60
Answer:
for him it send 4 small packages it will cost 9.20
For him to send 6 large packages it will cost 23.40
23.40 + 9.20 = 32.60
Step-by-step explanation:
Formula: Quanity x Cost = Total
After Totals + Costs = Exact Total
Select the correct answer from each drop-down menu. A triangle ABC with base AC is shown. A line DE, parallel to line AC, passes through vertex B. Interior angle at vertex A is labeled 1, at vertex C is labeled 3, and at vertex B is labeled 2. The exterior opposite angles at vertex B are 4 and 5. Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°. Statement Reason Points A, B, and C form a triangle. given Let be a line passing through B and parallel to . definition of parallel lines ∠3 ≅ ∠5 and ∠1 ≅ ∠4 m∠1 = m∠4 and m∠3 = m∠5 m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line m∠1 + m∠2 + m∠3 = 180° substitution
The statement to prove that the sum of the interior angles of ΔABC is 180° should be completed as follows;
Statements Reasons
Points A, B, and C form a triangle. ⇒ Given
Let DE be a line passing through B and parallel to AC. ⇒ definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4 ⇒ alternate interior angle theorem.
m∠1 = m∠4 and m∠3 = m∠5 ⇒ congruent angles have equal measures.
m∠4 + m∠2 + m∠5 = 180° ⇒ angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° ⇒ substitution
What is the congruence of angles?In Mathematics, congruence of angles can be defined as a theorem which states that two (2) angles are congruent when the measure of their angles are equal.
This ultimately implies that, two (2) congruent angles would always have equal measures as depicted in triangle ABC with line DE;
m∠1 = m∠4 and m∠3 = m∠5
By applying the Alternate Interior Angles Theorem to triangle ABC and line DE, we have the following:
∠3 ≅ ∠5 and ∠1 ≅ ∠4
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A ball is dropped from the top of a building 74 ft tall, How long will it take to fall to ground level?
To determine how long it will take for a ball to fall from the top of a building 74 ft tall to ground level, we can use the formula:
t = √(2*d/g)
where t is the time in seconds, d is the distance in feet, and g is the acceleration due to gravity (approximately 32.2 ft/s^2 on Earth).
Plugging in the values:
t = √(2*74 / 32.2)
t ≈ 3.63 seconds
So the ball will take approximately 3.63 seconds to fall to the ground level.
It's important to note that this calculation assumes that there's no air resistance and the ball is dropped vertically. In reality, air resistance and the ball's trajectory would affect the time it takes to fall.
Ramiro earns $20 an hour during the week and $30 an hour for overtime on the weekends. one week, ramiro earned a total of $650. he worked a total of 30 hours, including both weekday and weekend hours. determine how many hours of overtime Ramiro worked on the weekend.
Part A: Define your variables
Part B: Write two equations for this scenario
Part C: determine how many hours of overtime ramiro worked
The number of hours Ramiro worked overtime is 5 hours.
How to represent situation with equation?Ramiro earns $20 an hour during the week and $30 an hour for overtime on the weekends.
One week, Ramiro earned a total of $650. he worked a total of 30 hours, including both weekday and weekend hours.
The number of hours Ramiro worked on the weekend can be calculated as follows;
using equation,
let
x = number of hours worked during the week
y = number of hours worked during overtime
Hence,
20x + 30y = 650
x + y = 30
multiply equation(ii) by 20
20x + 30y = 650
20x + 20y = 600
subtract the equations
10y = 50
y = 50 / 10
y =5
Therefore, the number of hours worked overtime is 5 hours.
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A scale factor of 7 is it an enlargement reduction or neither
A scale factor of 7 is it an enlargement neither.
What is scale factor?Scale factor is a ratio of two corresponding lengths, areas, or volumes of similar shapes. When two shapes are similar, one can be enlarged or reduced to create the other. The scale factor is the number by which a figure is multiplied or divided to form a similar figure. It is used in many areas of mathematics, including geometry, trigonometry, and algebra. It is also used in engineering and architecture to create drawings of scaled-down or scaled-up objects.
A scale factor of 7 does not necessarily indicate an enlargement or reduction; it simply states that the size of an object has been multiplied by a factor of 7. It could either increase or decrease the size of the object, depending on the original size of the object and the direction of the scale factor.
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Which function represents the graph of f (x) = 1/2 (3)^x
The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value.
How do you find the function of a graph?The graph of a relation is said to reflect a function if a vertical line drawn anywhere on the graph only intersects the graph once. A graph does not reflect a function if a vertical line can cross it at two or more places. Linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs fall under this category. Write the equation in the form y = mx + b to determine the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept (0, b). Plot the y-intercept next. 3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.To learn more about function refer to:
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Solve the compound inequality. 3x+2≤8 or 4x+4>24
Answer:
x<2 or x>5
Step-by-step explanation:
3x+2<8 4x+4>24
4x>24-4
3x<8-2
4x>20
3x<6
x>5
x<2
Answer: x∈(-∞,2]U(5,∞)
Step-by-step explanation:
[tex]\displaystyle\\\left [ {{3x+2\leq 8} \atop {4x+4 > 24}} \right. \ \ \ \ \left [ {{3x\leq 6\ (1)} \atop {4x > 20}\ (2)} \right.[/tex]
Divide both parts of the equation (1) by 3 and divide both parts of the equation (2) by 4:
[tex]\displaystyle\\\left [ {{x\leq 2} \atop {x > 5}} \right. \\\\Hence,\\\\x\in(-\infty,2]U(5,\infty)[/tex]
LESSON 7 SESSION 2
Develop Using the Standard Algorithm
to Add and Subtract Decimals
Read and try to solve the problem below.
How much greater is the mass of a dollar coin than the combined
masses of a dime and a quarter?
TRY
IT
put
Math Toolkit base-ten blocks, base-ten grid paper,
grid paper, number lines, place-value charts
Mass of U.S. Coins
Periny: 2.5 g
Dime: 2.268 g
Nicket: 5. g
Quarter: 5.67 g
Half-Dollar: 11.34 g Dollar 8.1 g
Exploring Base Ten Blocks : Measure 1 x 1 x 1 cm with units of "ones."
Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.
Hundred times flats Count 1 cm by 10 cm by 10 cm.
Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.
How do you solve a base ten block?Our base ten number system is spatially represented by Base Ten Blocks. The four separate concrete representations known as "Base Ten Blocks" are generally used in middle school arithmetic after being introduced in elementary school.
Measure 1 x 1 x 1 cm with units of "ones."
Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.
Hundred times flats Count 1 cm by 10 cm by 10 cm.
Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.
When names are given based on shape rather than value, it is possible to rename the pieces as needed. For instance, a class learning decimals can use the flat to represent a unit and then determine the value of the other components.
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1.On the accompanying grid, sketch the graphs of y = 2^x and 3y = 7x + 3 over the interval
-3 ≤ x ≤ 4. Identify and state the coordinates of all points of intersection.
As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.
what are coordinates ?When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.
given
y = 2^x and 3y = 7x + 3 over the interval -3 ≤ x ≤ 4.
as x = -3
y = 2^x= 2^-3 = -8
y = 8
3y = 7x+3
3y= 7*-3 +3
3y = -21 + 3
y = -6
As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.
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NO LINKS!!
Write an equation to represent the following graphs:
a. passes through (-2, 18.75 and (1, 1, 1.2)
a-value:___________ b-value:____________
Equation: _____________________
b. passes through (0, 6) and (2, 8.64)
a-value:_____________ b-value:_____________
Equation:________________________
Answer:
[tex]\textsf{a)\;\;passes\;through\;$(-2, 18.75)$\;and\;$(1, 1.2)$}[/tex]
[tex]\textsf{$a$-value:\;\;3 \quad $b$-value: \;\;0.4}[/tex]
[tex]\textsf{Equation: \quad $y=3 (0.4)^x$}[/tex]
[tex]\textsf{b)\;\;passes\;through\;$(0, 6)$\;and\;$(2, 8.64)$}[/tex]
[tex]\textsf{$a$-value:\;\;6 \quad $b$-value: \;\;1.2}[/tex]
[tex]\textsf{Equation: \quad $y=6 (1.2)^x$}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (a)Given points:
(-2, 18.75)(1, 1.2)Substitute both points into the exponential function formula to create two equations:
[tex]\textsf{Equation\;1}: \quad 18.75=ab^{-2}[/tex][tex]\textsf{Equation\;2}: \quad 1.2=ab[/tex]Divide the equations to eliminate a, then solve for b:
[tex]\implies \dfrac{18.75}{1.2}=\dfrac{ab^{-2}}{ab}[/tex]
[tex]\implies15.625=\dfrac{b^{-2}}{b}[/tex]
[tex]\implies15.625=b^{-2}b^{-1}[/tex]
[tex]\implies15.625=b^{-3}[/tex]
[tex]\implies15.625=\dfrac{1}{b^{3}}[/tex]
[tex]\implies b^{3}=\dfrac{1}{15.625}[/tex]
[tex]\implies b=0.4[/tex]
Substitute the found value of b into the second equation and solve for b:
[tex]\implies 1.2=0.4a[/tex]
[tex]\implies a=3[/tex]
Therefore, the exponential equation is:
[tex]y=3 (0.4)^x[/tex]
-------------------------------------------------------------------------------------------
Part (b)Given points:
(0, 6)(2, 8.64)Substitute point (0, 6) into the exponential function formula and solve for a:
[tex]\implies 6=ab^0[/tex]
[tex]\implies 6=a(1)[/tex]
[tex]\implies a=6[/tex]
Substitute the found value of a and point (2, 8.64) into the exponential function formula and solve for b:
[tex]\implies 8.64=6b^2[/tex]
[tex]\implies b^2=\dfrac{8.64}{6}[/tex]
[tex]\implies b^2=1.44[/tex]
[tex]\implies b=\sqrt{1.44}[/tex]
[tex]\implies b=1.2[/tex]
Therefore, the exponential equation is:
[tex]y=6 (1.2)^x[/tex]
A quadrilateral with vertices (2, 5) and (-3, -4) has point symmetry about the origin.
a. What transformation maps the quadrilateral onto itself?
b. What are the other two vertices of the quadrilateral?
The transformation that maps the quadrilateral into itself is [-1 0] and [ 0 -1] and the vertices of the quadrilateral is (-3,-4),(2,5),(-2,-5),(3,4)
What is Transformation of the Quadrilaterala. A point symmetry about the origin is a transformation that maps a figure onto itself by reflecting it across the origin. This transformation is known as a central reflection or an isometry, and it is represented by the matrix (with respect to the standard basis)
[-1 0]
[ 0 -1]
b. To find the other two vertices of the quadrilateral, we can apply the transformation to the given vertices.
The transformation maps (2,5) to (-2,-5) and (-3,-4) to (3,4).
So, the other two vertices of the quadrilateral are (-2,-5) and (3,4)
So the quadrilateral will be (-3,-4),(2,5),(-2,-5),(3,4)
Note that a quadrilateral with point symmetry about the origin is called a kite.
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Fuel consumption is commonly measured in miles per gallon (mi/gal). An agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. Find the range, variance, and standard deviation for the sample data. Is the decrease of 4 mi/gal unusual? Why or why not? 2 1 2 1 3 3 4 2 2 2 2 2 2 2 2 3 2 2 2 2 2 The range of the sample data is mi/gal. (Type an integer or a decimal.) The variance of the sample data is . (Round to one decimal place as needed.) mi/gal. The standard deviation of the sample data is mi/gal.
(Round to one decimal place as needed.) Is the largest decrease, 4 mi/gal, unusual? Why or why not? O A. The decrease of 4 mi/gal is unusual because the smallest value in a data set is usually an outlier. O B. The decrease of 4 mi/gal is unusual because it is more than two standard deviations from the mean. O C. The decrease of 4 mi/gal is not unusual because the sample is a simple random sample, in which no values are considered unusual. O D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean.
A. The range of the sample data is 4 mi/gal.
B. The variance of the sample data is 0.98 mi/gal.
C. The standard deviation of the sample data is 0.99 mi/gal.
D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean (4 mi/gal is less than 2*0.99 mi/gal).
A. To find the range of the sample data, we need to find the difference between the largest and smallest values in the sample. In this case, the largest value is 4 mi/gal and the smallest value is 1 mi/gal. The range is the difference between these two values, which is 4 mi/gal - 1 mi/gal = 3 mi/gal.
B. To find the variance of the sample data, we first need to find the mean of the sample. The mean is calculated by summing all the values in the sample and dividing by the number of values in the sample. In this case, the mean is [tex]\frac{(2+1+2+1+3+3+4+2+2+2+2+2+2+2+2+3+2+2+2+2+2)}{20} = 2.05[/tex].
Next, we need to subtract the mean from each value in the sample, square the result, and divide it by the number of values in the sample. The variance is
[tex][(2-2.05)^2 + (1-2.05)^2 + (2-2.05)^2 + (1-2.05)^2 + (3-2.05)^2 + (3-2.05)^2 + (4-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (3-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2] = 19.6[/tex]
[tex]\frac{19.6}{20} = 0.98 mi/gal.[/tex]
C. To find the standard deviation, we take the square root of the variance. The standard deviation is [tex]\sqrt{0.98} = 0.99 mi/gal[/tex]
D. The standard deviation measures the amount of variation or dispersion in the data. The standard deviation is used to determine how much the values in a sample differ from the mean. If a value is more than two standard deviations away from the mean, it is considered unusual. In this case, the value of 4 mi/gal is less than 2*0.99 mi/gal = 1.98 mi/gal away from the mean, so it is not considered unusual.
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serious reply for finding the function to f(x+1)=3x squared +4x-2
The numeric value of the function f(x) = 3x² + 4x - 2 at x = x + 1 is obtained as follows:
f(x + 1) = 3x² + 10x + 3.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = 3x² + 4x - 2
The numeric value at x = x + 1 is found replacing both instances of x by x + 1, hence:
f(x + 1) = 3(x + 1)² + 4(x + 1) - 2
f(x + 1) = 3(x² + 2x + 1) + 4x + 4 - 4
f(x + 1) = 3x² + 6x + 3 + 4x
f(x + 1) = 3x² + 10x + 3.
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2. Solve for BC using Law of Sines. Round to the nearest tenth when necessary
Answer:
the answer to the question is 9.9 in the nearest tenth
You deposit $120 in an investment account that earns 6.4% annual interest compounded quarterly write a function that represents the balance y (in dollars) of the investment account after t years y= ? What is the balance of the account after 6 years
Answer:1200
Step-by-step explanation:
Answer:
[tex]\textsf{Function:} \quad y=120\left(1.016\right)^{4t}[/tex]
The balance of the account after 6 years is $175.64 (nearest cent).
Step-by-step explanation:
To write a function that represents the balance y (in dollars) of the investment account after t years, substitute the given values into the compound interest formula.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
A = yP = $120r = 6.4% = 0.064n = 4 (quarterly)t = t yearsSubstitute these values into the formula:
[tex]\implies y=120\left(1+\dfrac{0.064}{4}\right)^{4t}[/tex]
[tex]\implies y=120\left(1+0.016\right)^{4t}[/tex]
[tex]\implies y=120\left(1.016\right)^{4t}[/tex]
To calculate the balance of the account after 6 years, substitute t = 6 into the function:
[tex]\implies y=120\left(1.016\right)^{4 \cdot 6}[/tex]
[tex]\implies y=120\left(1.016\right)^{24}[/tex]
[tex]\implies y=120\left(1.46368961...\right)^{24}[/tex]
[tex]\implies y=175.642753...[/tex]
Therefore, the balance of the account after 6 years is $175.64 (nearest cent).
For a goodness-of-fit test, the frequencies obtained from the performance of an experiment are the:
i) subjective frequencies
ii) observed frequencies
iii) expected frequencies
iv) objective frequencies
Option B : observed frequencies are the frequencies obtained from the performance of an experiment for a goodness-of-fit test .
The frequency, or outcomes, that are gathered during an experiment are known as observed frequencies. This is frequently the collection of data that is documented in mathematics. The distinction between an observed frequency and an expected frequency is described on the display poster. Counts derived from experimental data are known as observed frequencies. In other words, you really take measurements when the data is being collected. For instance, you might roll a die ten times and then tally the number of times each number appears. Following the experiment, the count is made. The observed frequencies are these numbers, and the sign for an observed frequency is O. There are k entries in the table. There are n total observed frequencies. Calculating predicted frequencies involves multiplying the probability.
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Rain fell at a constant rate for 212 hours on Friday. During that time, the total amount of rain that fell was 34 inch. What is the rate, in inches per hour, at which rain fell during that time on Friday?
a 313
b 178
c 815
d 310
The rate, in inches per hour, at which rain fell during that time on Friday is 3/10 inches per hour.
Option d is the answer
How to determine the rate, in inches per hour, at which rain fell during that time on Friday?Rate is the ratio that compares two quantities of different units. It can be used to express how fast something is changing, or how much of one quantity is present for a certain amount of another quantity.
In this case, the rate, in inches per hour, at which rain fell during that time on Friday will be:
rate = (3/4) / (2 1/2)
rate = 3/10 inches per hour
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Complete Question
Rain fell at a constant rate for 2 1/2 hours on Friday. During that time, the total amount of rain that fell was 3/4 inch. What is the rate, in inches per hour, at which rain fell during that time on Friday?
a 3 1/3
b 1 7/8
c 8 1/5
d 3/10
Juan has a blueprint of a professional basketball court. The scale is 1 inch to 4 feet. If the
professional basketball court is 50 feet wide, how wide is the drawing of the court on the blueprint?
Use the questions below to help you solve.
a. Write the scale as a ratio.
b. Use your answer from part (a) and the information in the problem to write a scale
proportion.
c. Solve the scale proportion you wrote in part (b) to determine the width of the
professional basketball court in the blueprint. Show all your work.
Answer:
a. The scale is 1 inch to 4 feet. This can be written as a ratio: 1:4
b. Using the ratio from part a, the scale proportion is: 1/4 = width of the drawing/50 feet
c. To find the width of the drawing, we will use cross multiplication and solving for the width, we have 1/4 * 50 feet = width of the drawing/50 feet = 1* 50/4 =12.5 inches.
The width of the drawing on the blueprint is 12.5 inches.
Step-by-step explanation:
The answer to each part is mentioned below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Juan has a blueprint of a professional basketball court. The scale is 1 inch to 4 feet and the professional basketball court is 50 feet wide.
After the dilation, the relation between final and initial dimensions of the image is -
y = Kx
where -
{K} is a dimensionless quantity called scale factor.
{a} -
the scale as a ratio can be written as -
K = (1 inch/4 feet) = (1/12 feet/4 feet) = (1/48) = 1 : 48
K = 1 : 48
{b} -
We can write the scale proportion as -
(1/48) = (x/50)
{c} -
The width of the professional basketball court in the blueprint is -
x = 50/48
x = 1.05 feet
Therefore, the answer to each part is mentioned above.
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Improper fraction 2x2/3
PLEASE HELP
The graph for the equation y = 2 x minus 2 is shown below.
On a coordinate plane, a line goes through points (0, negative 2) and (1, 0).
If another equation is graphed so that the system has one solution, which equation could that be?
y = 2 (x + 1)
y = 2 (x minus 1)
y = 2 (x minus 2)
y = negative 2 (x + 1)
From the graph solution of system of equations is (0, -2). Therefore, option D is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given equation is y=2x-2.
Graph the line using the slope and y-intercept, or two points.
Slope: 2
y-intercept: (0, -2)
Now,
A) y=2(x+1)
2x-2=2(x+1)
No solution
B) y=2(x-1)
2x-2=2(x-1)
No solution
C) y=2(x-2)
2x-2=2(x-2)
No solution
D) y=-2(x+1)
2x-2=-2(x+1)
2x-2=-2x-2
4x=0
x=0
Substitute x=0 in y=-2(x+1), we get y=-2
Therefore, option D is the correct answer.
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z is a standard normal random variable. The P(-1.5 < z < 1.09) equals
a. 0.7953.
b. 0.4322.
c. 0.0711.
d. 0.3621.
If z is a standard normal variable then the probability of P(-1.5 < z < 1.09) is 0.79533
Here it is given that Z is a standard normal variable. This imples that the mean of Z is 1 and the standard deviation is 0. Hence we get
μ = 1
σ = 0
Now we need to find the probability P(-1.5 < z < 1.09)
We know that P(a < X < b) = P(X < b) - P(X < a)
= P(z < 1.09) - P(z < -1.5)
We know that P(x < -a) = 1 - P(x < a)
= P(z < 1.09) + P(z < 1.5) - 1
Now looking up the s-score for 1.09 and 1.5 in the z-table we get
0.86214 + 0.93319 - 1
= 0.79533
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a warehouse 40 yards long, and 25 yards wide, and it is piled with cartons to a height of 3 yards. what is the area of the warehouse floor? what is the total volume of the cartons? (assume there is no space between cartons.)
The area of the warehouse floor is 1000 square yards. This can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.
What is the calculated ?The calculated answer is the result of a mathematical equation or calculation. Calculations can range from simple addition and subtraction to complex integrations and derivatives. By using mathematical formulas, equations, and algorithms, the calculated answer can be used to solve problems and make predictions. Calculated answers can be used in fields such as science, engineering, economics, and finance. Calculated answers can also be used to make decisions about investments, projects, and other business decisions. In addition, calculated answers can be used to analyze data and make decisions based on the results.
The area of the warehouse floor is 1000 square yards. This can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.
The total volume of the cartons is 12500 cubic yards. This can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. Therefore, in this case V = 40 x 25 x 3 = 12500.
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what is the equation
-8x+10y=16
-4x-5y=13
The equations give values of 1/2 and -11/8
What is simultaneous equation?you should be aware that two equations are solved simultaneously if they are solved together
The given equations are
-8x+10y=16 .............................1
-4x-5y=13 ..................................2
Multiply equation 2 by 2 to have
-8x -10y=26
Subtract equation 1 from equation 2
-8x+10y=16
-(-8x-10y=26) To get
The we have 20y = 10
Make y the subject of the relation
y=1/2
Put y = 1/2 in equation 1
-8x +10(1/2) = 16
-8x +5 = 16
-8x = 16-5
-8x = 11
Making x the subject of the formula we have
x=-11/8
In conclusion the values of x and y are -11/8 and 1/2 respectively
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-2x+3=-7x-37
Solve for x
Answer:
x=-8
Step-by-step explanation:
Follow the steps in the image.
-Hope this Helped
i need help with this
Speed data were collected at a section of highway during and after utility maintenance work: The speed characteristics are given as_ and as shown below. Determine whether there was any significant difference between the average speed at the 95% confidence level (Z-1.96). The standard deviation of the difference in means is given as gd {( 012 n) - 022 n2)} DATA: uavh = 35.5 mph uav2 = 38.7 mph 2.5 mph =74 mph 250 n2 280
The standard deviation of the difference in means is (-1.96, 1.96). There is no significant difference between coverage speed at 95%
The speed characteristics are given as_
[tex]$$ \begin{aligned}\bar{x}_1 & =35.5 & \bar{x}_2 & =38.7 \\\sigma_1 & =7.5 & \sigma_2 & =7.4 \\n_1 & =250 & n_2 & =280\end{aligned}$$[/tex]
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero.
Standard deviation, denoted by the symbol σ, describes the square root of the mean of the squares of all the values of a series derived from the arithmetic mean which is also called the root-mean-square deviation.So
[tex]$$\begin{aligned}z=\frac{\overline{x_1}-\bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}} & =\frac{35.5-38.7}{\sqrt{\frac{(7.5)^2}{250}+\frac{(7.4)^2}{280}}} \\& =\frac{-3.2}{\sqrt{0.225+0.1956}} \\& =\frac{-3.2}{0.64852} \\\z & =-4.9343\end{aligned}$$[/tex]
at 95% confidence acceptance region is: [tex]$$(-1.96,1.96)[/tex]
But [tex]$z \notin(-1.96,1.96)$[/tex]
So, there is no significant difference between coverage speed at 95%.
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The standard deviation of the difference in means is 0.4696 and acceptance region is (-1.96 , 1.96). So, there was no significant difference between the average speed sample data at the 95% confidence level.
Speed data was collected on a section of road during and after repair work. Now the significance level for mean rate = 95% = 0.95 The equation for the standard deviation of the mean difference is:
σd = √(σ₁²/n₁ + σ₂²/n₂).
For the first data sample,
Sample mean for average velocity, X₁
= 35.5 mph
sample size, n₁ = 250
standard deviation, σ₁ = 2.5 mph
sample seconds, sample mean for
average velocity, X₂ = 38.7 mph
sample size, n₂ = 280
standard deviation, σ₂ = 7.4 mph.
It is statistically significant to see if there is a difference between the two population means. Using the two sample Z =( X₁-bar - X₂-bar )/√(σ₁²/n₁) + (σ₂²/n₂)}
Substituting all known values,
Z = ( 35.5 - 38.
7 )/(2,5)²/250 + (7,4)²/280
=> Z = - 3,2/√0,025 + 0.1956
=> Z = -3.2/0.4696
=> Z = - 6.8832
95% confidence interval, tolerance range is (-1.96, 1.96). However, Z∉(-1.96 , 1.96)
So, there is no signification difference for means between avaerage speed at 95%.
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Complete question :
Speed data were collected at a section of highway during and after utility maintenance work: The speed characteristics are given as, and as shown below. Determine whether there was any significant difference between the average speed at the 95% confidence level (Z=1.96). The standard deviation of the difference in means is given as σd = √(σ₁²/n₁ + σ₂²/n₂). DATA: uav₁= 35.5 mph, uav₂= 38.7 mph ,σ₁ = 2.5 mph, σ₂= 7.4 mph n₁ = 250, n₂ = 280
I need the expression for h(x)
Answer:
h(x) =-5x^2 -1
Step-by-step explanation:
same function just move down 3 so y intercept changes only and 2-3= -1.
which equations are equivalent to -2y+3/2x+7/4
a) -1/2xy+7/4
b) 3/2x-2(y+7/2)
c) -1/4y+3/2 (y+x)
d-2y+1/2(3x+7/2)
e) 1/4 (-8y+6x+7)
The equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7). The solution has been obtained by using the simplification method.
What is simplification?
Simplifying in mathematics refers to the process of working with and understanding an equation in a way that makes it more understandable or transparent. The process of grouping similar terms together so that the problem can no longer be solved further is known as simplification.
We are given -2y + 3/2x + 7/4
In order to find which expression is equivalent to the given, we need to simplify the expressions.
a. -1/2xy+7/4
This is not the same expression as given.
b. 3/2x-2(y+7/2)
⇒ 3/2x - 2y - 7
This is not the same expression as given.
c. -1/4y+3/2 (y+x)
⇒ -1/4y + 3y/2 + 3x/2
This is not the same expression as given.
d. -2y+1/2(3x+7/2)
⇒ -2y + 3x/2 + 7/4
This is the same expression as given.
e. 1/4 (-8y+6x+7)
⇒-2y + 3x/2 + 7/4
This is the same expression as given.
Hence, the equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7).
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ASAP HELP ME!! A florist is preparing for a wedding reception. He will need to use 12 roses to make a small bouquet for each round table. He will also need to use 36 roses for a huge centerpiece for the wedding party's long table. Write an equation that shows how the total number of roses used, y, depends on the number of round tables, x.
A possible equation to represent the total number of roses the florist will need to use in this situation is 36 + 12x= y.
What is an equation?This is a short mathematical expression that relates variables represented by letters by using mathematical symbols such as +, -, x, and the symbol =.
What elements should the equation include?The equal symbolThe variables represented by lettersOther mathematical symbols or numbers to correctly and completely represent the situationBased on this, a possible equation is 36 + 12x= y.
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