The solution for X is 5. An equation is a mathematical statement that shows the equality of two expressions.
It typically consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.
To solve for X, we first need to distribute the 5 to the expression in parentheses:
30 = 5X + 25
Then, we can isolate the variable term by subtracting 25 from both sides:
5 = 5X
Finally, we can solve for X by dividing both sides by 5:
X = 5
Therefore, the solution for X is 5.
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Please help I will give brainliest
The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).
What is Segment?
In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.
To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:
((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.
So, let's first find the coordinates of the midpoint of segment AB:
Midpoint = ((-3 + 7)/2, (2 - 10)/2)
= (2, -4)
Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:
((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)
= (-1/2, -1)
So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).
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On The Standard Normal Curve, The 68th Percentile Corresponds To The Mean Value Of The Data Set Is That True Or False
The 68th percentile on the standard normal curve corresponds to the mean value of the data set. This statement is false.
The 68th percentile on the standard normal curve corresponds to one standard deviation away from the mean. In other words, approximately 68% of the data falls within one standard deviation of the mean on the standard normal distribution. This is a property of the normal distribution, which is a continuous probability distribution commonly used in statistics.
To clarify, the mean value of a data set is the arithmetic average of all the values in the data set. It is not directly related to the 68th percentile on the standard normal curve. The mean is a measure of central tendency and is influenced by all the data values, while the percentile is a measure of relative position in the distribution of data.
Therefore, it is important to understand the difference between percentiles and measures of central tendencies, such as mean, median, and mode, when analyzing data using statistical techniques.
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According to the figure showing 2020 GDP for selected countries, how much larger (in percentage terms) is America's GDP than:
According to the figure showing 2020 GDP for selected countries, America’s GDP is 21.43% which is 7.19% larger than China’s GDP which is 14.24%.
A country's economic output is measured by its gross domestic product (GDP). GDP is estimated by totaling all the commodities and services produced in a nation within a predetermined time frame, typically a year. In 2020, America’s GDP was 21.43% of the total GDP of selected countries. This is 7.19% larger than China’s GDP which was 14.24% of the total GDP of selected countries.
We must use exchange rates to convert GDPs to a common currency in order to compare GDPs across nations. Once the GDPs are expressed in a similar currency, we can compare the GDP per capita of each nation by dividing the GDP by the population. Large GDPs are common in countries with big populations, although GDP is not always a reliable measure of a country's wealth. GDP per capita is a better metric.
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Complete question is:
According to the figure showing 2020 GDP for selected countries, how much larger (in percentage terms) is America's GDP than:
The G D Ps are as follow: United states, 21.43; China, 14.24; Japan, 5.08; Germany, 3.86; India, 3.87; Great Britain, 2.83; Russia, 1.70; Mexico, 1.27; Sweden, 0.53; Greece, 0.21; Haiti, 0.08.
Round your responses to the nearest whole number.
1. Russia?
______ % larger
2. Germany?
______ % larger
The accurate scale diagram shows a telephone mast and a box.
Find an estimate for the real height, in metres, of the telephone mast.
telephone mast
5.5
+2.5 m
box
+
Total marks: 2
Using proportions, the real height of the telephone mast is estimated to be 9 meters.
What exactly is a proportion?A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.
The following proportional relationship is established as a result:
x / 1.5 cm = 10.8 cm / 1.8 cm.
The relationship's left side can be simplified as follows:
6 = x / 1.5 cm.
The estimate is then calculated using cross multiplication, as shown below:
6 x 1.5 cm = 9.5 cm².
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A rectangle measures 3 2/3 inches by 1/2 inches. What is its area?
the rectangle has a surface area of 11/6 square inches and perimeter is 23/3 inches.
How is area and perimeter determined?We must multiply the length by the width of the rectangle to determine its area. Applying the provided metrics, we have:
Area is equal to the product of length and width.
Area is equal to (11/3) x (1/2) inches.
11/6 square inches is the area.
As a result, the rectangle has a surface area of 11/6 square inches.
The lengths of all four sides must be added up in order to determine the rectangle's perimeter. Applying the provided metrics, we have:
Perimeter equals 2 (length plus width).
Perimeter equals 2 (3 2/3 inches plus 1 inch).
perimeter equals two (11/33 inch plus 1/2 inch).
P = 2 (or 23/6 inches)
Diameter is 23 3/8 inches.
As a result, the rectangle's perimeter is 23/3 inches.
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maria makes a quilting pattern with two similar isosceles triangles. in one triangle, the base is 1.4 in. and the other side lengths are each 3.2 in. find the length of each side, r, of the other triangle if its base is 4.48 in.
Answer:10.24
Step-by-step explanation: Since the triangles are similar, then
r/3x2= 4x48/1x4,
r=3.2x4.48=10.24
The bus depart by 8:30 because they want to start by 9:30. What time will the bus arrive at the beach if the bus ride takes 35 minutes?
The bus will arrive at the beach by 9:05 am. To calculate the arrival time of the bus, we need to add the travel time to the departure time.
First, we need to convert the departure time of 8:30 am to minutes.
8:30 am = 8 x 60 + 30 = 510 minutesThen, we add the travel time of 35 minutes to the departure time:
510 + 35 = 545 minutesFinally, we convert the arrival time back to hours and minutes:
545 ÷ 60 = 9 with a remainder of 5So the bus will arrive at 9:05 am.
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Jessica kicks a football. Its height in feet is given by h(t) = -16t^2+80t where h is the height and t is the time, in seconds, after the football is kicked. Graph the equation from t=0 to t=5 seconds. Be sure to include the vertex in your graph and table.
State the coordinates of the vertex and explain its meaning in the context of the problem.
The point is where the vertex is situated [tex](2.5, 100)[/tex].
What in math is a vertex?A vertex, which is a unique point on a mathematical object, is often where 2 or more lines or edges come together. The shapes that include vertices most frequently are graphs, polygons, polyhedra, and angles. Vertices in a graph are sometimes called nodes.
Vertex and parabola definitions.A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola which equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.
To graph the equation [tex]h(t) = -16t^2 + 80t[/tex] from [tex]t=0[/tex] to [tex]t=5[/tex] seconds, we can create a table of values by plugging in values of t and calculating the corresponding values of [tex]h(t)[/tex]:
t h(t)
0 0
1 64
2 128
3 144
4 128
5 80
To find the vertex, we can use the formula [tex]t = -b/(2a)[/tex], where [tex]a = -16[/tex] and [tex]b = 80[/tex].
[tex]t = -b/(2a) = -80/(2(-16)) = 2.5[/tex]
So the vertex occurs at [tex]t = 2.5[/tex] seconds.
Now we can plot the points from the table and graph the equation,
Graph of [tex]h(t)=-16t^2+80t[/tex] from [tex]t=0[/tex] to [tex]t=5[/tex] seconds
The vertex is located at the point [tex](2.5, 100)[/tex].
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Suppose the point (3, 6) is on the graph of y = f(x) What point does it transform to y = - f * (x) - 3 ?
Using the given variable, write an inequality to model the scenario.
Bowlers that score at least 228 points will make it to the next round.
Let p = the number of points
Answer:
p ≥ 228
Step-by-step explanation:
p ≥ 228
This inequality means the Bowlers have to score at least 228 points to move on.
Hope this helped!
How do you work this out?
Anyone help please .
Answer:
x=5/4 or x=5/9
pls mark me brainliest
Answer:
x=5/4 (for the first x),x=5/9 (for the second x)
Deon needs to read novels each month.
Let N be the number of novels Deon needs to read in M months.
Write an equation relating N to M. Then graph your equation using the axes below.
Equation can also be used to calculate how many novels Deon needs to read in a certain amount of months. For example, if the number of months is 4, then Deon needs to read 8 novels.
What is equation?An equation is a statement that expresses the relationship between two or more mathematical expressions. It is typically written in the form of an equality, such as "2x + 3 = 7", where "2x + 3" is the left-hand side and "7" is the right-hand side. Equations are used to model real-world problems and can be solved to determine the value of the unknowns within the equation.
The equation above shows that the number of novels Deon needs to read in a certain amount of months is twice the number of months. This can be graphically represented by a straight line, with a slope of 2, that passes through the origin on the graph. The graph below illustrates this equation. The x-axis represents the number of months (M) and the y-axis represents the number of novels (N). As the number of months increases, the number of novels Deon needs to read also increases, at a rate of 2 novels per month.
This equation can also be used to calculate how many novels Deon needs to read in a certain amount of months. For example, if the number of months is 4, then Deon needs to read 8 novels.
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For this problem, determine whether the following sets of vectors spanR3, and feel free to use Octave for your calculations. (a)⎩⎨⎧100,021,103⎭⎬⎫(b)⎩⎨⎧110,300⎭⎬⎫(c)⎩⎨⎧101,310,−100,215⎭⎬⎫
The vectors in set (c) span R3.Answer: (a) The vectors span R3, (b) The vectors do not span R3, (c) The vectors span R3.
To solve this problem, you need to determine if the given sets of vectors spanR3 or not. You may use Octave for your calculations.Here are the sets of vectors: (a) S1 = { [1; 0; 0], [0; 2; 1], [1; 0; 3] }(b) S2 = { [1; 1; 0], [3; 0; 0] }(c) S3 = { [1; 0; 1], [3; 1; 0], [-1; 0; 0], [2; 1; 5] }To determine whether the vectors in the given sets span R3, you can place the vectors in a matrix as column vectors and compute the rank of the matrix. If the rank is 3, then the vectors span R3. Otherwise, they do not.
(a) S1 = { [1; 0; 0], [0; 2; 1], [1; 0; 3] }R1 = [1 0 1; 0 2 0; 0 1 3]rank(R1) = 3The rank of R1 is 3, so the vectors in set (a) span R3.
(b) S2 = { [1; 1; 0], [3; 0; 0] }R2 = [1 3; 1 0; 0 0]rank(R2) = 2The rank of R2 is 2, so the vectors in set (b) do not span R3.
(c) S3 = { [1; 0; 1], [3; 1; 0], [-1; 0; 0], [2; 1; 5] }R3 = [1 3 -1 2; 0 1 0 1; 1 0 0 5]rank(R3) = 3The rank of R3 is 3, so the vectors in set (c) span R3.Answer: (a) The vectors span R3, (b) The vectors do not span R3, (c) The vectors span R3.
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(a) Factorise 25t²₋ 4
(b) Factorise x²₋6x₋3xy₊18y
Step-by-step explanation:
(a) To factorize 25t² - 4, we can use the difference of squares formula:
a² - b² = (a + b)(a - b)
In this case, a = 5t and b = 2. So we have:
25t² - 4 = (5t + 2)(5t - 2)
Therefore, 25t² - 4 can be factorized as (5t + 2)(5t - 2).
(b) To factorize x² - 6x - 3xy + 18y, we can group the terms:
(x² - 3xy) - (6x - 18y)
We can then factor out the common factors from each group:
x(x - 3y) - 6(x - 3y)
Notice that both terms have a factor of (x - 3y), so we can factor it out:
(x - 3y)(x - 6)
Therefore, x² - 6x - 3xy + 18y can be factorized as (x - 3y)(x - 6).
(a)
.
in this case, a= 25t and b= 4.
.
ans: (5t-4)(5t+4)
4. Find the solution of the following equations:
a) x + 5 = 15
b) 12 – y = 12
c) 3a = 27
d) y/4 = 20
e) 2 + y = 0
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 8 times out of 10 attempts. Tasha has hit the ball 9 times out of 12 attempts. Which player has a ratio that means they have a better batting average?
Tasha, because she has the lowest ratio since 0.75 < 0.8
Tasha, because she has the highest ratio since 48 over 60 is greater than 45 over 60
Jana, because she has the lowest ratio since 0.75 < 0.8
Jana, because she has the highest ratio since 48 over 60 is greater than 45 over 60
Jana, because she has the highest ratio since 8/10 is greater than 9/12.
What is ratio?A ratio is a comparison of two numbers or quantities expressed in relation to each other. It represents the relative size or magnitude of one quantity with respect to another. Ratios are typically written as a fraction, with the first number being the numerator and the second number being the denominator, and can also be expressed as a decimal or percentage.
What is batting average?Batting average is a statistical measure used in baseball to evaluate a player's performance at the plate. It is calculated as the ratio of a player's total number of hits to their total number of at-bats (the number of times they attempt to hit the ball).
In the given question,
A higher batting average indicates a better performance, since it means the player is successfully hitting the ball more often.
In this case, we are given the number of hits and attempts for two players, Jana and Tasha. To compare their batting averages, we need to calculate the ratio of their hits to their attempts.
Jana has hit the ball 8 times out of 10 attempts, so her batting average is 8/10 = 0.8.
Tasha has hit the ball 9 times out of 12 attempts, so her batting average is 9/12 = 0.75.
To determine which player has the better batting average, we compare their ratios. Since 0.8 is greater than 0.75, Jana has the higher ratio and therefore the better batting average.
So, the answer is Jana, because she has the highest ratio (8/10 = 0.8), which means she has the better batting average compared to Tasha (9/12 = 0.75).
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a cyclist rides her bike at a speed of 21 kilometers per hour. what is this speed in kilometers per minute? how many kilometers will the cyclist travel in 2 minutes? (do not round the answer)
Answer:
see the answer and explanation in the attached figure below
Step-by-step explanation:
In the past 5 years company A sold 7.5x10^4 reams of paper. Company B sold 9.5 x10^3 reams. How many total reams did they sell altogether and how many more did company a sell than B?
Giving 20 pts please help!
84500 reams of paper are the total amount the two companies sell in the past five years.
65500 is the amount that Company B performed better than company A.
What is a Company?A company can be defined as the part in which the main aim or goal is to earn a profit. This was to generate the income that they will be having in the firm. There are various employees that are present in the company and work towards a common goal.
The Amount that is made by company A is
[tex]7.5 \times 10000[/tex]
[tex]=75000[/tex]
The amount of paper manufactured by company B is
[tex]= 9.5 \times 1000[/tex]
[tex]= 9500[/tex]
A) The total that is made by both companies in 5 years will be
[tex]= \text{Company A + Company B}[/tex]
[tex]= 75000 + 95000[/tex]
[tex]= 84500[/tex]
B) Company B made better products as compared to Company A
[tex]= \text{Company B - Company A}[/tex]
[tex]=75000 - 9500[/tex]
[tex]=65500[/tex]
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Answer:
total: 84,500 or 8.45×10⁴difference: 65,500 or 6.55×10⁴Step-by-step explanation:
You want the sum and difference of 7.5×10^4 and 9.5×10^3.
Scientific notationNumbers are most conveniently added or subtracted in scientific notation when the multipliers have the same exponent. For this we can rewrite Company B's volume as ...
9.5×10^3 = 0.95×10^4
total sales = 7.5×10^4 + 0.95×10^4 = 8.45×10^4 = 84,500
difference in sales = A -B = 7.5×10^4 -0.95×10^4 = 6.55×10^4 = 65,500
__
Additional comment
You can enter the numbers "as is" in a calculator or spreadsheet and format the output in whatever form you need.
Geometry Altitudes Questions
The value for the height h of the right triangle is equal to 4.8990.
How to evaluate for the value of h for the triangleThe height h of the right triangle divides the triangle in two triangles with the same proportions as the original triangle, which implies that if the adjacent for the smallest triangle is 4 and the adjacent of the other triangle is h, then:
h/6 = 4/h {considering the tangent ratio}
h² = 4 × 6 {cross multiplication}
h = √24
h = 4.8990
Therefore, value for the height h of the right triangle is equal to 4.8990.
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dr carl is a mathematics and statistics lecturer. he is interested in studying a new approach at teaching mathematics and statistics in high school. recently this new approach has been adopted. it was previously the case that the mean score for all high school students doing their end of year exam was 71, however, the population standard deviation is unknown. the scores of all students are approximately normally distributed. he thinks that, with this new teaching approach, the mean score may have increased. a random sample of 39 scores is gathered and the sample mean and standard deviation calculated. dr carl will conduct a hypothesis test using a level of significance of 0.01. select the correct null and alternative hypotheses for this test:
The test is one-tailed to the right due to the Alternate hypothesis.
In a hypothesis test, a Null hypothesis (H0) is a statement of "no effect" or "no difference," whereas the Alternate hypothesis (HA) is a statement of "some effect" or "some difference." Here are the correct null and alternative hypotheses for the given scenario: Null hypothesis: H0: μ = 71, Alternative hypothesis: HA: μ > 71 (One-tailed test) we have a one-tailed hypothesis test since the research hypothesis is directed. In a one-tailed test, we're looking for a difference in one direction only. In this case, Dr Carl thinks that there has been an improvement, so the alternative hypothesis reflects this. Therefore, the test is one-tailed to the right.
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Solve for x in the triangle.
Answer:
D. 87
Step-by-step explanation:
You want to know the measure of the angle opposite the longest side in a triangle with side lengths 13, 16, and 20 inches.
Angle relationsThe angle x is opposite the side of length 20 inches in this triangle, which is the longest side. That tells you x is the largest angle.
The largest angle in any triangle is never less than 60°. This eliminates all answer choices except the last one:
x = 87
Law of CosinesIf you want to go to the trouble to solve the triangle, the law of cosines is helpful. For sides a, b, c and angle C, it tells you ...
c² = a² +b² -2ab·cos(C)
Solving for the angle, we have ...
C = arccos((a² +b² -c²)/(2ab))
C = arccos((13² +16² -20²)/(2·13·16)) = arccos(25/416) ≈ 86.55°
x ≈ 87
determine the dew point temperature, the humidity ratio, the specific volume and the enthalpy given a dry bulk temperature of 39oc and a wet bulb temperature of 18oc.
The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.
To determine the dew point temperature, the humidity ratio, the specific volume and the enthalpy given a dry bulk temperature of 39°C and a wet bulb temperature of 18°C, you can use a psychometric chart or a specialized software program that calculates these properties based on the given dry bulb and wet bulb temperatures, as well as other relevant parameters such as pressure, altitude, and air composition.
First, plot 39°C (the dry bulk temperature) and 18°C (the wet bulb temperature) on the chart. Then mark The atmospheric pressure of 101.325 kPa, the dew point temperature is approximately 10.4°C, the humidity ratio is approximately 0.0084 kg of water vapor per kg of dry air, the specific volume is approximately 0.85 m³/kg of dry air, and the enthalpy is approximately 91 kJ/kg of dry air.
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in an examination, 90 % of the students passed out of 600 students. how many candidates passed the exam?
Answer:
Step-by-step explanation:
[tex]90 \% \text{ of }600=\frac{90}{100}\times600[/tex]
[tex]=90 \times 6[/tex]
[tex]=540[/tex]
So 540 students passed the exam.
(Find the Smallest Value) Write an application that finds the smallest of several integers. Assume that the first value read specifies the number of values to input from the user.
To find the smallest of several integers, you will need to write a program that takes in a number of values specified by the user as input, and then outputs the smallest value. First, you will need to create a loop that reads in the number of values specified by the user. To do this, you can use a 'for' loop that reads in the values until it reaches the user-specified number of values. Inside the loop, you can create a variable to store the smallest value and compare each value to the smallest value to determine if it is smaller. If the value is smaller, then the smallest value should be updated.
Finally, once the loop has gone through all of the values, the smallest value should be outputted. In summary, to find the smallest value of several integers, you will need to use a 'for' loop to read in the specified number of values from the user, compare each value to the smallest value, and update the smallest value if it is smaller. Then, you can output the smallest value once the loop is complete.
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i am a parallelogram with a longer sides 15 cm each and a shorter sides 8m each my perimeter is
Answer:
Step-by-step explanation:
= 2(15+8)
=2(23)
=46
F= (y + 2x, 2x + 5z, 7y + 8x), C is the circle with radius 5, cen- ter at (2,0,0), in the plane x = 2, and oriented counterclockwise as viewed from the origin (0,0,0).
The set of points that represent the intersection of the curve of vector function F and circle C is
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t ranges from 0 to 2π}.
We have,
Vector function F = (y + 2x, 2x + 5z, 7y + 8x)
C is the circle with radius 5, center at (2,0,0), in the plane x = 2
C is oriented counterclockwise as viewed from the origin (0,0,0)
The vector function F represents a three-dimensional curve in space.
The circle C is a two-dimensional object in space, lying in the plane x = 2 and centered at (2,0,0) with a radius of 5. It is also oriented counterclockwise as viewed from the origin (0,0,0).
To find the intersection of vector function curve F and circle C, we can substitute the equation of the circle into the equation of the curve and solve for the parameter(s) that satisfy the equation. However, since the equation of the circle is given in terms of x only, we can simplify the equation of the curve by substituting y = 0 and z = 0:
F = (2x, 2x, 8x)
Now, we can substitute x = 2 + 5cos(t) and y = 5sin(t) (the parameterization of the circle C in the plane x = 2) into the equation of the curve F:
F = (2(2+5cos(t)), 2(2+5cos(t)), 8(2+5cos(t)))
= (4+10cos(t), 4+10cos(t), 16+40cos(t))
Thus, the intersection of vector function curve F and circle C is given by the set of points:
{(4+10cos(t), 4+10cos(t), 16+40cos(t)) | t in [0, 2π)}
Note- that the parameter t represents the angle of rotation around circle C, and ranges from 0 to 2π to cover the entire circle.
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A landscaper needs to mix a 80% pesticide solution with 35 gal of a 30% pesticide solution to obtain a 55% pesticide solution. How many gallons of the 80%
solution must he use?
By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.
What is equation?In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
Let's say a landscaper needs to use x gallons of an 80% pesticide solution.
The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.
After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.
Since we need a 55% pesticide solution, we can set the following formula:
[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]
Therefore, landscapers should use 35 gallons of an 80% pesticide solution.
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the height of a diver above the water, is given by , where is time measured in seconds and is measured in meters. select all statements that are true about the situation. a. the diver begins 5 meters above the water. b. the diver begins 3 meters above the water. c. the function has 1 zero that makes sense in this situation. d. the function has 2 zeros that make sense in this situation. e. the graph that represents starts at the origin and curves upward. f. the diver begins at the same height as the water level.
Statement (b) and (c) are true about the situation.
Define the term measurement ?Using standardized instruments or units, measurements are the process of figuring out the size, quantity, or degree of anything.
Using the given function, h(t) = -5t^2 + 10t + 3, we can determine the true statements about the situation:
a. False: The diver begins at h(0) = 3 meters above the water, not 5 meters.
b. True: The diver begins at h(0) = 3 meters above the water.
c. True: The function has one zero that makes sense.
To find it, we set h(t) = 0 and solve for t: -5t² + 10t + 3 = 0
Using the quadratic formula, we find that: t ≈ 2.161
This means that the diver reaches a height of zero after 2.161 seconds.
d. False: As we found in part (c), the function has only one zero.
e. False: The graph of the function does not start at the origin.
f. False: The diver begins at 3 meters above the water, not at the same height as the water level.
Therefore, statement (b) and (c) are true about the situation.
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Complete question-
When solving the equation 3(x-2)=-12, what is a possible first step?
A) Distributing the 3 into each term of the parenthesis.
B) She could either divide by 3 or distribute 3 into the parenthesis
C) Adding 2 to each side of the equation
D) Subtracting 2 on each side of the equation
E) Dividing each side of the equation by 3
F) none of the answer choices tell what the first step could be.
Suppose that the speed at which cars go on the freeway is normally distributed with a mean of 66 miles per hour (mph) and standard deviation 10 mph. Letxxbe the speed for a randomly selected car. Round all answers to 4 decimal places where possible.What is the z-score for a car that is caught going 60 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going below 60 mph?P(x≤60)=P(x≤60)=What is the z-score for a car that is caught going 86 mph? The z-score =What is the probability of randomly choosing a car on the freeway and it going above 86 mph?P(x≥86)=P(x≥86)=If a highway patrol woman only wants to catch the top 1% of all cars on the freeway , then what speed does the car on the freeway need to be going in order for her want to catch the speeder? mph
To catch the top 1% of all cars on the freeway, the speed of the car needs to be greater than 99 mph. This is because 99 mph is three standard deviations above the mean, which would put it in the top 1% of speeds.
The question asks for the z-scores and probabilities of cars going 60 mph and 86 mph on the freeway. It also asks for the speed at which the highway patrol woman needs to catch the top 1% of cars.
Let xx be the speed for a randomly selected car on the freeway, with a mean of 66 mph and standard deviation of 10 mph.
The z-score for a car that is caught going 60 mph is -2.0000. This means that the car is two standard deviations below the mean. The probability of randomly choosing a car on the freeway and it going below 60 mph is 0.0228.
The z-score for a car that is caught going 86 mph is 2.0000. This means that the car is two standard deviations above the mean. The probability of randomly choosing a car on the freeway and it going above 86 mph is 0.0228.
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