The label on a car's antifreeze container claims to protect the car between -40°C and 125°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C = 5/9 (F - 32). Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.

With the help of Pythagoras Theorem for triangles, we get that the possible areas of the square are: 12 sq. units and 20 sq. units, according to the cases mentioned.

According to the Pythagoras Theorem, in a right angled triangle, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given:

Sides of a right triangle are 2 and 4 units.

To find: Area of a square that shares a side with the third side of the triangle.

Finding:

There can the following cases:

If 2 and 4 units are the lengths of the perpendicular sides.

Then, by Pythagoras Theorem, -

[tex]H^{2} = 2^{2}+4^{2}\\ H^{2} = Side^{2}\\H=Side \\H= \sqrt{4+16} \\H= \sqrt{20} \\H= 2\sqrt{5}[/tex]

Hence, the area of the square = side² = 20 units²

If 4 units is the length of hypotenuse.

Then, by Pythagoras Theorem,

[tex]4^{2} = 2^{2} + A^{2} \\16 - 4 = A^{2} \\= \sqrt{12}\\[/tex]

side of triangle = [tex]\sqrt{12}[/tex]

Hence, the area of the square = side² = 12 units²

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In 3 hours Tom drives 243 miles.

So, to find how many miles Tom can drive in 3 hours:

Given: Tom drives 81/2 miles every 1/30 hour.

So, in 30 minutesTom drives 40.5 miles.

Therefore, Tom drives 243 miles in 3 hours.

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Answer: A. is true.

Step-by-step explanation: The left side 16384 is equal to the right side 16384, which means that the given statement is always true.

The property of equality justifies the given statement is Transitive property of equality.

Given,

The statement:

If, 7x = 28,

then, x = 4

We have to find the property of equality that justifies this statement:

The transitive property of equality formula is given as follows:

If y = z and x = y, x must be z. Where items belong to the same category as x, y, and z. For instance, if a line segment's measurement is represented by "x," then its measurement should also be represented by "y" and "z."

The property of equality that justifies this statement If, 7x = 28,

then, x = 4 is  transitive property of equality.

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Answer:

what you have to do is multiply 2 times 4 which is 8 and multiply the 8 by 9 which is 72

Step-by-step explanation:

2*4 =8

8*9=72

72 plus 8 is 80

Answer:

x = -7
x = -3

Step-by-step explanation:

Given the following question:

[tex]2\left|x+5\right|=4[/tex]

To find the answer to this question we have to remember to apply the absolute value. The absolute value means we have to convert any negative within the lines into positive.

[tex]2\left|x+5\right|=4[/tex]
[tex]\frac{2\left|x+5\right|}{2}=\frac{4}{2}[/tex]
[tex]\left|x+5\right|=2[/tex]
Apply absolute value:
[tex]x+5=-2[/tex]
[tex]x+5=2[/tex]
Solve each equation:
[tex]x+5=-2[/tex]
[tex]5-5=0[/tex]
[tex]-2-5=-7[/tex]
[tex]x=-7[/tex]
[tex]x+5=2[/tex]
[tex]5-5=0[/tex]
[tex]2-5=-3[/tex]
[tex]x=-3[/tex]


Your answers are "x = -3 and x = -7."

Hope this helps.

Answer:

x = -3

x= -7

Step-by-step explanation:

l x + 5 l = 4/2

(x + 5) = 2 or - (x + 5) = 2

- (x + 5) - 5 = 2 - 5

x = -3

- x - 5 = 2

- x - 5 + 5 = 2 + 5

-x = 7

x = -7

The average of the other 3 numbers is 72.

Average or mean is a measure of central tendency which calculates the central point of a data-set.

Average of a set of numbers is calculated by taking the sum of the numbers and dividing it by the total frequency of the numbers.

If 3 numbers a , b and c are taken then the average is equal to

(a+b+c) ÷3

Given average of 5 numbers is 72.

Therefore the sum of the numbers is  72 × 5 = 360

Two of the numbers are 70 and 74 .

Sum of the remaining 3 numbers = 360 - (70 + 74) = 360 - 144 = 216

Average of the 3 numbers = 216 ÷ 3 = 72

Therefore the average of the remaining 3 numbers is 72.

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Answer:

241.5

Step-by-step explanation:

201.96+38.7+0.84

The two methods for estimation of the quotient of 538 divided by 96 is being explained.

We are given that:

538 ÷ 96

We need to estimate the quotient of 538 ÷ 96 by using two methods.

The first method can be that we first estimate the divisor and the dividend to the nearest tens and then perform the division.

538 will be rounded off to 540 and 96 will be rounded off to 100.

So, it becomes:

540 ÷ 100

= 5.4

This will again be rounded off to 5

= 5

The second method will be that we first perform the division and then round off.

538 ÷ 96 = 5.61

Rounding off, we will get:

= 6.

Therefore the two methods for estimation of the quotient of 538 divided by 96 is being explained.

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The equation 2⁻³ = 0.125 in logarithmic form is -3log(2) = log(0.125)

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Given the equation:

2⁻³ = 0.125

Taking the logarithm of both sides:

log(2⁻³) = log(0.125)

-3log(2) = log(0.125)

The equation 2⁻³ = 0.125 in logarithmic form is -3log(2) = log(0.125)

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Let's use Trigonometric ratios to find p :

[tex]\qquad \sf  \dashrightarrow \: \cos(60) = \cfrac{6}{p} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{2} = \dfrac{6}{p} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 6 \times 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 12 \: \: units[/tex]

Based on the calculation below, the rate at which the weeds grow each day is 0.7%.

Given:

f(x) = 3(1.05)x = 3(1 + 0.05)x ................... (1)

Since there are 7 days in a week, the rate at which the weeds grow each day can be calculated from equation (1) by dividing 0.05 (i.e. 5% weekly growth rate) as follows:

f(x) = 3(1 + (0.05 / 7))x

f(x) = 3(1 + 0.007)x

f(x) = 3(1.007)x

Since 0.007 is the same as 0.7%, this implies that the rate at which the weeds grow each day is 0.7%.

The correct option is "f(x) = 3(1.007)7x; spreads at a rate of approximately 0.7% daily".

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Answer: Option 1

Step-by-step explanation: Correct for my test.

Answer:

Part A: 28.26t²

Part B: 2,826 square unit

Explanation:

Part A:  

A[p(t)] = π (3t)² = 3.14 * 9t² = 28.26t²

Part B:

p(10) = 3(10) = 30

A(p) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit

Answer:

down below

Step-by-step explanation:

The picture is a little blurry so the graph is hard to read. But I believe the answer is 7/8. The rose would be counting up or down the y axis and the run is counting forward or backward on the x axis.

Hope this helps! :)

Answer:

rise = 7, run = 8

slope = rise/run = 7/8

See attached picture for graph in case you have to plot

Step-by-step explanation:

Take two distinguishable points, (x1, y1) and (x2, y2)  on the graph. Find the difference in their y values= y2 - y1. This will be the rise

Find the corresponding difference in the x values, x2 - x1. This will be the run

Divide the y difference by the x difference and you get rise/run which is the slope of the line

Two clear points are (x1 = 0, y1= -7) and (x2=8, y2=0)

(y2 - y1)/(x2 - x1)

= (0 - (-7)/(8 - 0))

= (0+7/(8 - 0)             ==> 2 negatives make a positive

= 7/8  and that is rise/run

Rise = 7, run = 8

Picture shows rise and run if you want to graph it

The two such x-values are 2 and 8.

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Answer:

b. No

Step-by-step explanation:

7/6 can be changed to an equivalent ratio(fraction) by multiplying by the same number on top and on the bottom.

example:

7/6 = 7×3 / 6×3

= 21/18

21/18 is equivalent to 7/6.

7 doesn't even go into 52 for one thing. But 6×8 is 48 so try 8.

7/6 = 7×8 / 6×8

= 56/48

56/48 is equivalent to 7/6, not 52/48

We get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.

We want to change the digit in the number 5,341 into 5,841.

We also need to find the difference between the numbers.

The number 3 is in the 3rd place (hundreds) of the number 5,341 as a digit will be replaced by 8  to form the number 5,841.

This means that 300 is replaced by 800 because the third place in both the numbers is of hundreds.

The difference between 800 and 300 is:

800 - 300 = 500.

Subtraction of 5,341 from 5,841 also yields 500.

Therefore, we get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.

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Answer:

The question is incompleye. Do elaborate?

Required probability = 120 * 0.0010819 =  0.1298

total number of outcomes of 7 from 10 = 10*9*8 / 3*2*1  = 120

probability of each outcoe is 0.85^7* (0.15)^(3)  = 0.0010819

Required probability = 120 * 0.0010819 =  0.1298

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.

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Answer:7lb

Step-by-step explanation:

7x180=1260lb

1260+235=1495lb

Answer:

84:56

Step-by-step explanation:

a:b:c

(7:8)

( 12:7)

Answer:

A:C = 3:2

Step-by-step explanation:

A:B = 7:8 is a proportion relationship and can be represented using fractions:

[tex]\displaystyle{\frac{A}{B} = \frac{7}{8}}[/tex]

Similarly the proportion relation B:C = 12:7 can be represented as:
[tex]\displaystyle{\frac{B}{C} = \frac{12}{7}}[/tex]

Multiply the first equation by the second
[tex]\displaystyle\frac{A}{B}\;\mathsf{x}\;\frac{B}{C} = \frac{7}{8}\;\mathsf{x}\;\frac{12}{7}[/tex]

This evaluates to
[tex]\displaystyle\frac{A}{C} = \frac{12}{8}[/tex]

Simplifying gives us
[tex]\displaystyle\frac{A}{C} = \frac{3}{2}[/tex]

So A:C = 3: 2

Answer:

[tex]d=1/2[/tex]

How to solve:

Step-by-step explanation:

[tex]\frac{5}{6}=\frac{1}{3}+d\\\frac{1}{3}+d=\frac{5}{6}[/tex]

Group

[tex]\frac{1}{3}+d=\frac{5}{6}\\\frac{1}{3}+d-\frac{1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1}{3}+\frac{-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{0}{3}=\frac{5}{6}-\frac{1}{3}\\d+0=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}+\frac{-1\cdot 2}{3\cdot 2}\\d=\frac{5}{6}+\frac{-1\cdot 2}{6}\\d=\frac{5}{6}+\frac{-2}{6}\\d=\frac{5-2}{6}\\d=\frac{3}{6}\\d=\frac{1\cdot 3}{2\cdot 3}\\d=\frac{1}{2}[/tex]

Hope it helps.

Answer: 17 times

Step-by-step explanation:

It takes 6 times for the first recipe (.25x6=1.5)

It takes another 11 times for the second recipe (.25x4=2 + .25x3 = 0.75)

You add 6 + 11 and get 17

Answer:

1 solution

Step-by-step explanation:

2y + 20y - 15 = 19 + 20y , that is

22y - 15 = 19 + 20y ( subtract 20y from both sides )

2y - 15 = 19 ( add 15 to both sides )

2y = 34 ( divide both sides by 2 )

y = 17

Answer:

Step-by-step explanation:

Answer

one

Proof

2y + 20y - 15 = 19 + 20y             Combine the left side.

22y - 15 = 19 + 20y                      Add 15 to both sides

22y - 15+15 = 19 +15 + 20y          Combine

22y = 34 + 20y                            Subtract 20y from booth sides

22y-20y = 34 + 20y-20y             Combine

2y = 34                                          Divide both sides by 2

2y/2 = 34/2

y = 17

That's the only solution you get. The number of solutions to any equation (with certain exceptions) is the highest power on the variable.

x^2 + 2x - 8    has 2 solutions (from the x^2)

x^3 + 3x^2 + 2x + 15 = y has three solutions

(a) Slope of AB =    and Slope of CD =

(b) True, both segments are not parallel as they lie on the same line

(c) Distinct lines are the words in Parallel slope property that addresses the problem in part(b).

What is Slope of a line and Parallel Slope Property and co-linear points?

Slope of a line :Given are two points P (x₁, y₁) and Q ( x₂, y₂)

Then slope of the line  PQ is given by  [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Given Parallel Slope Property: Two  distinct lines are parallel if the have the same slope

Colinear points: A,B,C,D are collinear points if the slopes of lines AB, BC,CD,DA are all equal.

Given the points A(-5,-2), B(1,1), C(-1,0), and D(3,2).

Slope of the line AB [tex]=\frac{1-(-2)}{1--(5)}=\frac{3}{6} =\frac{1}{2}[/tex]

Slope of the line CD [tex]=\frac{2-0}{3-(1)}=\frac{2}{4} =\frac{1}{2}[/tex]

Slope of the line BC [tex]=\frac{0-1}{-1-1}=\frac{-1}{-2} =\frac{1}{2}[/tex]

Slope of the line DA=[tex]\frac{-2-2}{-5-3}=\frac{-4}{-8} =\frac{1}{2}[/tex]

Therefore A,B,C,D are collinear means they lie on the same lines

Slopes of AB and CD are equal but still they  are not parallel because according to Parallel Slope Property two lines with same slope are parallel only when they are distinct but AB and CD are on same line.

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Answer:

25 students and 40%

Step-by-step explanation:

False

• Correlation means that there is a relationship or patter between the two variables. A scatter plot displays the data about the two variables as a set of points in the x-y plane and it is a useful tool for determining if there is a correlation between the variables.

• Causation means the one event causes other event to occur. It can only be determined by designed experiment.

• While correlation and causation both can exist at the same time, correlation doesn’t imply causation.

• Causation explicitly applies only to cases where action P causes outcome Q whereas correlation is simply a relationship.

Correlation doesn’t prove causation.

There could be third variable associated with the size of engine which caused the truck to have greater horsepower. For example, it can be that manufacturers anticipate that consumers who wanted trucks with greater horsepower also prefered trucks with larger engines and therefore chooses to make trucks with larger horsepower.

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