Alex and Bev sat six tests, each with 50 marks.
The table shows their mean percentages after five tests.
Alex
60%
Bev
52%
After all six tests, their mean percentages were equal.
In the sixth test, Alex scored 24 out of 50
Work out Bev's score, out of 50, in the sixth test. ​

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

In the Triangle BCD, Angle B is 90° since tangent and radius are perpendicular to one another.

Now, let's find Angle C using Angle sum property of a triangle.

[tex]\qquad \tt \dashrightarrow \:\angle C + \angle B + \angle D = 180[/tex]

[tex]\qquad \tt \dashrightarrow \:\angle C + 90 + 45= 180[/tex]

[tex]\qquad \tt \dashrightarrow \:\angle C + 135= 180[/tex]

[tex]\qquad \tt \dashrightarrow \:\angle C= 180 - 135[/tex]

[tex]\qquad \tt \dashrightarrow \:\angle C= 45 \degree[/tex]

Now, we know that Angle made by an arc on the centre is twice the Angle made by same arc on boundary of circle, hence we can infer that :

[tex]\qquad \tt \dashrightarrow \:2\angle C = 10x[/tex]

[tex]\qquad \tt \dashrightarrow \:10x = 2 \times 45[/tex]

[tex]\qquad \tt \dashrightarrow \:x = 90 \div 10[/tex]

[tex]\qquad \tt \dashrightarrow \:x = 9[/tex]

So, the required value of x is 9

Answer:

$109.875

Step-by-step explanation:

Assuming "a pair" means 4 tires the math would be as follows:

146.50 for 4 tyres.

146.5/4 = cost of one tyre.

1 tyre: $36.625

Multiply by 3 for price of three tires:

36.625 x 3 = $109.875

Answer:

125 dollars

Step-by-step explanation:

Answer: C

Step-by-step explanation:

What is an Inequality?

The dictionary defines an inequaltiy as a statement that two quantities are unequal, indicated by the symbol ≠; alternatively, by the symbol <, signifying that the quantity preceding the symbol is less than that following, or by the symbol >, signifying that the quantity preceding the symbol is greater than that following.

Inequality for this problem

x > 6

The prism shown consists of 6 parallelograms and the surface area of the prism shown in the figure is 48 square inches.

The surface area is equal to the sum of all the areas of the sides of the figure.

The figure shown consists of 6 parallelograms. The area for calculating the area of a parallelogram is expressed as:
Area = Base * Height

Surface area = 4(2*4) + (4 * 4)
Surface area = 4(8) + 16
Surface ares = 48 square in

Hence the surface area of the prism is 48 square inches.

Learn more on surface area of prism here: https://brainly.com/question/1297098

Step-by-step explanation:

I think the answer is 15cm

The equation of the line of best fit is an illustration of a linear function

The teenager would spend $9 on food if he or she is at the mall for three hours.

The equation of the line of best fit is given as:

y = 2x + 3

When the teenager spends 3 hours in the mall, it means that:

x = 3

So, we have:

y = 2 * 3 + 3

Evaluate the product

y = 6 + 3

Evaluate the sum

y = 9

Hence, the teenager would spend $9 on food if he or she is at the mall for three hours.

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Answer:

a

Step-by-step explanation:

Answer:

$5.67

Step-by-step explanation:

All you have to do is 17 divided by 3 to figure out how much it costs for one hour, that equals 5.666, but you have to round it to the nearest cent, which equals 5.67. ;)

Answer:

It is(-1,5)

Step-by-step explanation:

You just divide the (-3,15) by 3 and you get your answer.

Answer:

(-1 , 5)

Step-by-step explanation:

Find the coordinates of the point after dilation:

A (-1,5) and B (-3,4)

The square MATH has equal side lengths MA, TH, AT and HM

Hanna's claim is correct because

The coordinate points are given as:

M(1, 2), A(-5, 3), T(-6,-3), and H(0,- 4).

Calculate the side lengths of the square using the following distance formula

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have:

MA = √[(1 + 5)^2 + (2 - 3)^2] = √37

AT = √[(-5 + 6)^2 + (3 + 3)^2] = √37

TH = √[(-6 + 0)^2 + (-3 + 4)^2] = √37

HM = √[(0 - 1)^2 + (-4 - 2)^2] = √37

The side lengths are equal.

Next, we calculate the slopes using:

m =(y2 - y1)/(x2 - x1)

So, we have:

MA = (2-3)/(1+5) = -1/6

AT = (3+3)/(-5+6) = 6

TH = (-3+4)/(-6+0) = -1/6

HM = (-4-2)/(0-1) = 6

See that opposite sides have the same slope

i.e MA = TH and AT = HM

And adjacent sides have their slopes to be opposite reciprocals

i.e. MA = -1/AT and TH = -1/HM

The calculated distances and slopes implies that Hanna's claim is correct

Read more about quadrilaterals at:

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Answer: The number is 14.

Step-by-step explanation:

14 minus 2 equals 12 and 12 times 5 equals 60.

Hope this helps :)

Have a great day!!

The value that will have the most dots displayed in the dot plot created for the data set is: C. 5

To create a dot plot, construct a horizontal line to label the values in the data set, then use dots to indicate the frequency in which each of the data points appear.

Given the data set:

2, 5, 5, 1, 4, 6, 2, 3, 5, 6, 3, 1, 4, 6, 1, 5

1 will have 3 dots

2 - 2 dots

3 - 2 dots

4 - 2 dots

5 - 4 dots

6 - 3 dots

Thus, the value with the most dots displayed would be: 5.

Learn more about dot plot on:

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Answer:

Step-by-step explanation:

Brenna rolled a number cube 16 times and recorded                                 each roll. the data are listed below.                                                                  2, 5, 5, 1, 4, 6, 2, 3, 5, 6, 3, 1, 4, 6, 1, 5                                                         create a dot plot for the data set. which value has the                               most dots displayed above it?

O A) 1

O B) 3

O D) 6

4 of the 5 is more 2 of the 2, 2 of the 3, 2 of the 4, 3 of the 1, 3 of the 6

So The Answer is C) 5

The percentage of children who have a birthday party at home between 5

and 10 is 3.69 %

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying by 100.

The percentage change is also calculated using the same method.

In percentage change we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Total number of children = 325

The number of children that have parties at home between the 5 - 10 age group.

= 12

Now,

The percentage of children who have a birthday party at home between 5

and 10.

= 12/325 x 100

= 3.69 %

Thus,

The percentage of children who have a birthday party at home between 5

and 10 is 3.69 %

Learn more about percentages here:

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#SPJ7

Answer:

A) use a straightedge to draw a line thought D and F

Step-by-step explanation:

got it right on the test

Answer:

Use the straightedge to draw the line through points C and D.

Step-by-step explanation:

i took quiz

Answer:

The ratio of the length opposite to the side of the triangle whose angle is opposite to the length of the hyptoneuse.

The solution of the inequality 2(4x - 3) ≥ -3(3x) + 5x is true for all x such that its a real number bigger or equal to 0.5 (Option A: x ≥ 0.5)

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

The considered inequality is:

[tex]2(4x - 3) \geq -3(3x) + 5x[/tex]

Simplifying its both sides, we get:

[tex]2(4x - 3) \geq -3(3x) + 5x\\8x-6\geq -9x + 5x\\8x-6 \geq -4x[/tex]

Adding 4x on both the sides, we get:

[tex]8x-6+4x \geq -4x + 4x\\(8+4)x - 6 \geq 0\\12x -6 \geq 0\\[/tex]

Adding 6 on both the sides, and dividing by 12, we get:

[tex]12x-6 +6 \geq 0+6\\12x \geq 6\\12x/12 \geq 6/12\\x \geq 0.5[/tex]

(some operations like addition, subtraction, multiplication by positive real number or division by positive real number keeps the inequality relation unaltered. With the use of such operations, here we tried to get x on one side, and constants on other side).

Thus, the considered inequality is true for all the values of x which are real numbers bigger or equal to 0.5 (Option A: x ≥ 0.5)

Learn more about inequalities here:

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Answer:

I can t see it

Step-by-step explanation:

Answer: hopefully this helps it’s a formula sheet for different shapes and it seems like your working with circles so use this!

Step-by-step explanation:

Answer:

Area = 84.1

OR Exact A = 392 - 98pi

Step-by-step explanation:

Calculate the area of the rectangle and subtract the area of the two circles. See image.

Answer:

[tex] \frac{560}{7} = 80[/tex]

[tex]80 \times 20 = 1600[/tex]

Hillary read 80 word every min

so, 80 × 20 =1600 word every 20 min

Answer: A) 2.4 ÷ 6

Step-by-step explanation:

      To answer this problem, we need to find the original whole and what it is being divided by.

[] The whole is 2.4 because we see two wholes shaded in, and 4 columns shaded in. For this model, it represents 2.4

[] It is being divided into 6 parts. This is shown with the white numbers and the thicker lines

      We can also check with math, 2.4 divided by 6 is 0.4 so it "checks out."

      This model represents the expression A) 2.4 ÷ 6.

Answer:

45 g

Step-by-step explanation:

30/200 simplified = 3/20

3/20 as a decimal = 0.15

0.15 g of barley for 1 ml of milk

300 · 0.15 = 45

45 g of barley for 300 ml of milk

hope this helps :)

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-4)}}}\implies \cfrac{-6}{1+4}\implies -\cfrac{6}{5}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-\cfrac{6}{5}}(x-\stackrel{x_1}{(-4)}) \implies y-5=-\cfrac{6}{5}(x+4) \\\\\\ y-5=-\cfrac{6}{5}x-\cfrac{24}{5}\implies y=-\cfrac{6}{5}x-\cfrac{24}{5}+5\implies y=-\cfrac{6}{5}x+\cfrac{1}{5}[/tex]

Answer:

1. 0.45

2. 0.06

3. 0.39

4. 7.77

Step-by-step explanation:

causeeeeeeee