Answer:
The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.
To find the magnification, we can divide the size of the image by the size of the object:
Magnification = size of image / size of object
Plugging in the values, we have:
Magnification = 85mm / 23mm
Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.
Step-by-step explanation:
write two equivalent expressions one exponential and one a product of factors, for 4 to the 5th power evaluate the expressions
Answer:
4^5 = 1024
4×4×4×4×4 = 1024
Step-by-step explanation:
An exponential expression is going to have an exponent representing the repeated multiplication. 4 times itself 5 times over is 4^5.
A product of factors is going to show the multiplication written out sort of in a long format:
4 × 4 × 4 × 4 × 4
4^5 = 1024
4×4×4×4×4 = 1024
The graph shows money in dollars as a function of time
in days. Write an equation for the function, and
describe a situation that it could represent. Include the
initial value, rate of change, and what each quantity
represents in the situation.
Each quantity represents in the situation are y is overall financial time (day). 10 times the daily wage earned. 25 times the money's initial worth.
What each quantity represents in the situation.The graph shows money in dollars as a function of time ,an equation for the function, and describe a situation that it could represent. Include the
initial value, rate of change
The slope is equal to 10 10 (simplify) = 175-75 / 15-5 100
y - 75 = 10(x - 5) (x - 5)
4 - 75 = 10x - 50 y - 75 + 75 = 10x - 10 + 75 y = 10x + 2.5
If you start with $25 and can make $10 every day, money do you have after x days are
y = overall financial time (day).
10 times the daily wage earned.
25 times the money's initial worth.
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area of 6ft 10ft 14ft figure
Answer:
209.25
Step-by-step explanation:
Calculate the areas of the triangle, rectangle, and half circle, then add them together:
triangle = 1/2bh = 1/2(6)(10) = 30
rectangle = bh = (14)(10) = 140
half circle = 1/2πr² = 1/2(3.14)(5)² = 39.25
radius = r = D/2 = 10/2 = 5
Total area = 30 + 140 + 39.25 = 209.25
Answer:
209.25 ft²
Step-by-step explanation:
To find the total area of the figure you have to add the areas of the triangle, rectangle and the semi circle.
Area of the triangle.
[tex] \sf \: A = \frac{1}{2} \times base \times height \\ \sf \: A = \frac{1}{2} \times 6 \: ft \times10 \: ft \\ \sf \: A = \frac{1}{2} \times 60 \: {ft}^{2} \\ \sf \: A =30 \: {ft}^{2} [/tex]
Area of the rectangle.
[tex]\sf \: A =length \times width \\ \sf \: A =14 \: ft \times 10 \: ft \\ \sf A =140 \: {ft}^{2} [/tex]
Area of the semi circle.
[tex] \sf \: A = \frac{1}{2} \pi {r}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times ( \frac{10}{2}) ^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times {5}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times 25 \\ \sf \: A = \frac{1}{2} \times 3.14 \times 25 \\ \sf \: A = \frac{1}{2} \times 78.5 \\ \sf \: A = 39.25 {ft}^{2} [/tex]
Add up all the areas to find the total area.
[tex] \sf \: Total \: Area = 30 {ft}^{2} + 140 {ft}^{2} + 39.25 {ft}^{2} \\ = 209.25 {ft}^{2} [/tex]
Sara is saving her money in a piggy bank
and counts it each month. The graph
shows her monthly savings. Choose any
two points and draw a slope triangle.
Dilate the slope triangle along the graph
to determine whether the amount Sara
saves each month is constant.
Answer: It is not possible for me to draw a slope triangle or dilate it along the graph without more information about Sara's monthly savings.
To determine whether the amount Sara saves each month is constant, you can choose any two points on the graph and use them to calculate the slope of the line connecting them. If the slope is constant for all pairs of points, then the amount Sara saves each month is constant. If the slope is not constant, then the amount Sara saves each month is not constant.
To calculate the slope of the line connecting two points, you can use the following formula:
slope = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
You can then use the slope triangle to visualize the slope of the line connecting the two points. If you dilate the slope triangle along the graph and the slope remains constant, then the amount Sara saves each month is also constant.
Step-by-step explanation:
A cake recipe calls for 2 1/3 cups of flour. If Gloria is planning on making 6 cakes for a bake sale, how many cups of flour will she need?
Answer: Gloria will need 14 cups of flour
Step-by-step explanation: 2 1/3 x 6 = 14
Convert the degree measure to radians or the radian measure to degrees. Then find one positive angle and one negative angle that is coterminal with the given angle.
1. -560°
2. 170°
-560° in radian is -28π/9 radian and the positive and negative coterminals are 8π/9 and -10π/9 respectively.
170° in radian is 17π/18 radian and the positive and negative coterminals are 53π/18 and -19π/18 respectively
How to convert the degree measure of angle to radians?An angle can be converted from degree to radian by multiplying it by π/180.
1. -560°
-560° × π/180 = -28π/9 radian
2. 170°
170° × π/180 = 17π/18 radian
In general, if θ is any angle in radian, then θ + n(2π) is coterminal angle with θ, for all nonzero integer n.
coterminal of -28π/9:
positive: -28π/9 = -28π/9 + 2(2π) = 8π/9
negative: -28π/9 = -28π/9 + 2π = -10π/9
coterminal of 17π/18:
positive: 17π/18 = 17π/18 + 2π = 53π/18
negative: 17π/18 = 17π/18 - 2π = -19π/18
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the number of geusts,g, coming for dinner is not 8
The number of guests, g, coming for dinner is not 8, is g ≠ 8.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
The expression,
the number of guests, g, coming for dinner is not 8.
That means,
Let the number is g.
According to the question,
the number is not equals to 8.
That means,
the expression in the numerator form,
g ≠ 8.
Therefore, the term in the mathematical form g ≠ 8.
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Which property is demonstrated below?
a times c = c times a
A.
associative property
B.
distributive property
C.
commutative property
D. identity property
Answer:
distributive property is your answer
Find the limits given based on the graph.
Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.
what are functions ?The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.
given
We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.
Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.
So in this case we can write:
limx → +∞f(x) = 0
limx → - ∞f(x) = 0
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Jocelyn has a collection of 100 coins. How many coins represent 25% of her collection?
25 coins represent 25 percent of Jocelyn's collection.
What is the percentage?A percentage is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.
given, Jocelyn has a collection of 100 coins.
100% of her collection represents = 100 coins
1 % of her collection represents = 100/100 coins
1% of her collection represents = 1 coin
thus,
25% of her collection represents = 1*25 coins
25% of her collection represents = 25 coins
therefore, 25 percent of the collection of Jocelyn represents 25 coins.
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Is the vertex of -x^2q-2x+10=0 parabola a maximum value or minimum value?
The vertex of the parabola -x² - 2x + 10 = 0 occurs at (-1,11), It is a maximum value.
Determine whether the parabola is maximum value or minimum value?Given the equation of the parabola;
-x² - 2x + 10 = 0
First, the maximum of a quadratic function occurs at;
x = -b/a, if a is negative, the maximum value of the function is f( -b/2a)
f_max(x) = ax² + bx + c occurs at;
x = -b/2a
Now, find the value of x = -b/2a
Plug in a = -1 and b = -2
x = -( -2/2(-1) )
x = -( -2/-2) )
x = -( 1 )
x = -1
Hence;
f(x) = -x² - 2x + 10
f( -1 ) = -( -1 )² - 2( -1 ) + 10
f( -1 ) = -1 + 2 + 10
f( -1 ) = -1 + 12
f( -1 ) = 11
Therefore, maximum occurs at (-1,11).
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If f(x)=2(x)^2+5square root (5+2) complete the following statement f(2)= blank
The complete statement is f(2) = 8+5√7
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here f(x)=2x²+5√7
Thus f(1) = 2×4+5√7
= 8+5√7
Hence, The complete statement is f(2) = 8+5√7
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6 divided 109 can you help?
Answer: 18.1666666667
Step-by-step explanation:
Q.
The surface area of a cube is
37.5 cm². What is the area of
each side of the cube?
The total surface area of the cube will be 37.5 cm²
What is the surface area of a cube?A three-dimensional shape's surface area is the sum of all of its faces. Finding the area of each face and adding them together gives us the surface area of a shape.Surface area analysis refers to the measurement of a particle's available surface. It is important because it is the means by which a solid interacts with its surroundings, whether they are gases, liquid, or other solids.Here the edge of the cube is given
Edge = 2.5 cm
We have to find out the total surface area of the cube
Total surface area of cube = 6a², where a is the edge of the cube
= 6 × 2.5 × 2.5
= 37.5 cm²
Hence, the total surface area of the cube will be 37.5 cm²
The complete question is,
Find the surface area of a cube of Edge 2.5 CM
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Write an equation of the line passing through (- 5,5) and having slope - 4. Give the answer in slope-intercept form.
The equation of the line in slope-intercept form is:
Answer:
y = - 4x - 15---------------------------
Slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptPoint-slope form:
y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point on the lineUse the point-slope form to find the equation and then convert it to slope-intercept form:
y - 5 = - 4(x - (-5))y - 5 = -4(x + 5)y - 5 = - 4x - 20y = - 4x - 20 + 5y = - 4x - 15Four gallons of paint are used to paint 25 chairs. If each chair used the same amount of paint, how many gallons are used to paint each?
Answer:
0.16 or 0.2 if rounded
Step-by-step explanation:
4 gallons divided by 25 chairs equals 0.16 gallons for each chair
hope this helps <3
Show 24÷1/4 step by step
Answer:
96
Step-by-step explanation:
24 divided by 1/4 is 96
you turn 24 into a fraction by putting a one under is and then you keep it change it flip it
24/1 Divided by 1/4
24/1 times 4/1
24 times 4= 96
1 times 1= 1
96/1=96
Five people each working eight hours a day can assemble 400 toys in a five day work week. What is the average number of toys assembled per hour per person?
Answer:
There are 5 people working and each person works 8 hours per day, so there are a total of 58 = <<58=40>>40 hours of work per day.
Over the course of the week, the total number of hours worked is 405 = <<405=200>>200 hours.
The total number of toys assembled is 400 and the total number of hours worked is 200, so the average number of toys assembled per hour per person is 400/200 = <<400/200=2>>2 toys per hour per person. Answer:{2}.
Step-by-step explanation:
Simplify the expression 3a² + 1/4a + 3 + a² + 4 + 1/4a
The Correct answer while simplifying the given algebraic expression is: 4a²+1/2a+7
What are Algebraic Expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Method to simplify any algebraic Expressions are :
By multiplying factors, remove any grouping symbols like brackets and parenthesis.If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.Add the constants togetherGiven:
=3a²+1/4a+3+a²+4+1/4a
=(3a²+a²)+(1/4a+1/4a)+(3+4)
=4a²+1/2a+7
So the Answer is
=4a²+1/2a+7
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Akira is setting tables at the restaurant where she works. She starts with a pile of 85 napkins, and she places 6 napkins on every table she sets
Write an equation that shows how the number of napkins remaining, y, depends on the number of tables akira sets, x
Answer: y = 85 - 6x
Step-by-step explanation:
Number of napkins remaining: y
Number of tables set: x
Akira starts out with 85 napkins. So, every time she sets a table, she is losing 6 napkins. The steady rate of napkins lost can be written with the following expression, as she is losing 6 napkins per table.
[tex]-6x[/tex]
These napkins are being removed from the total of 85 napkins:
[tex]85 - 6x[/tex]
The above equation also expresses the number of napkins remaining. Writing it as a proper equation:
[tex]y = 85 - 6x[/tex]
The final answer is: y = 85 - 6x
THIS ONE TOO PLEASE
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
The line going through the origin equation is also y=2x.
A line that crosses the origin is symbolized by the equation y=mx.
Also, y=2x satisfies the point (0,0)
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
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I need help with these 4 problems
As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.
Describe equation.A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 2x - 5 = 15 is an equation. We can find that the variable x has a value of 5 by resolving this equation.
Here,
In New York City, a one-bedroom apartment will cost $1600 in 2020.
Y = mx + c is frequently used as the formula for a straight line graph, where;
gradient = m
The vertical intercept is given by c.
With this knowledge, it is evident from the graph that y = 40x + 800 is the best line of fit for the data presented.
This indicates how much a one-bedroom apartment in New York City will cost in 2020, or 20 years after the year 2000.
y = 40(20) + 800 = $1600
As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.
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PLEASE HELP ME ASAP NOW PLEASE
The lines with a slope larger than f(x) are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which one is the linear equation shown on the graph?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
First, you can see that the line crosses the y-axis at y = -4, so the line is something like:
y = a*x - 4
And we can see that it crosses the x-axis at x = 2, then we can write the equation:
0 = a*2 - 4
4 = a*2
4/2 = a
2 = a
So the linear equation on the graph is:
y = 2*x - 4
The slope is 2, the linear equations with a slope larger than that are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which can be rewritten as:
y = (5/4)*16x - (5/4)*(1/2)
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2 points How Did I Do? The cost of renting a car is $42 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=42+0.25x , where x is the number of miles traveled.
The equation to represent the cost of renting the car, given the cost per week and the cost per mile, is y = 42 + 0.25x.
How to formulate the equation ?The total cost of renting the car at any given point, would be:
= Cost to rent per week + ( Cost per mile x Number of miles driven)
If we assume the number of miles driven is denoted by x, then the equation becomes :
= 42 + 0. 25 x
If we further take y to be the total cost, the equation then becomes :
y = 42 + 0. 25 x
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Please help I was sick and missed out on class thank you.
Answer: slope=-5 and y-intercept=1
Step-by-step explanation:
The equation given is in slope-intercept form. Slope-intercept for is y=mx+b, where m is slope and b is y-intercept.
This gives m=-5 and b=1.
A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of 12 centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of 58 bolts. The sample mean bolt length was 12.07 centimeters. The population standard deviation is known to be o=0.25 centimeters. what is the test statistic z? what is the p-value?
The test statistic from the factory population is 2.12. The p value is given as .017003.
How to solve for the test statisticsWe have the following values to solve the problem with
n = 58
sample mean x = 12.07
standard deviation = 0.25 meters
u = length = 12
The formula is given by
[tex]z= \frac{x-u}{sd/\sqrt{n} }[/tex]
when we insert the values we would have:
[tex]z= \frac{12.07-12}{0.25/\sqrt{58} }[/tex]
z = 0.07 / 0.033
z = 2.12
we have to find the p value when z = 2.12
The p value is 0.017003 using a statistical calculator
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Company A charges 125$ annual fee plus 7$ per hour car share fee. Company B charges 110$ plus 10$ per hour. What is the minimum number of hours that a car share needs to be used per year to make company a better deal?
Answer:
6
Step-by-step explanation:
Let the number of hours be [tex]x[/tex].
[tex]125+7x<110+10x \\ \\ 15+7x<10x \\ \\ 15<3x \\ \\ x>5[/tex]
So, the minimum is 6 hours.
Write an equation that represents the line. Use exact numbers
The equation of a line is y = 7/9x -3.5. using exact numbers from the graph.
What is the slope intercept of a line?
A straight line is produced by a linear function. Therefore, the slope has a constant value. If the slope was variable, a straight-line graph would not exist. When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b). The y value of the y-intercept point is denoted by the symbol b in the formula.
Given a line in the graph in that we can see that,
At x = 0, y is -3.5 and at y = 0, x is 4.5 thus,
coordinates of the given line are (0, -.35) and (4.5, 0)
Therefore the slope of the line (m) = (y₂-y₁)/ (x₂ -x₁)
The slope of the line = 3.5/4.5 = 7/9
therefore equation of the line in the slope-intercept form:
y = 7/9 x + c
Since this line passe from (0, -3.5)
hence, -3.5 = c
therefore, using exact numbers equation of the line is y = 7/9x -3.5.
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Eric picks 5/8 basket of strawberries. Kiki picks 1/5 basket of strawberries. Which answer is the most accurate estimate for how many more baskets of strawberries Eric picks than Kiki?
Eric picks 17/40 baskets of strawberries more than Kiki.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
Eric picks 5/8 basket of strawberries.
And, Kiki picks 1/5 basket of strawberries.
Hence, After subtraction we get;
Number of baskets of strawberries more than Kiki = 5/8 - 1/5
= (25 - 8) / 40
= 17/40
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a movie theater has 24 screens. ration of action to other films is 1:2. How many action films are currently showing
Answer: 12
Step-by-step explanation: Because of the ratio we know that half of the screens will be showing action films. Half of 24 is 12, so 12 screens will be playing action.