What is the relationship between the ratios?

5/8 and 8/10 are they proportional or not

Answer:

See below.

Step-by-step explanation:

We are asked for the diameter, radius, and area of a circle.

We are given the Circumference.

We should know that;

\(Circumference = (diameter)\pi\)

\(Circumference = 24\pi\) (Exact)

This means that the Diameter is 24.

The Radius is \(\frac{1}{2}\) of the Diameter.

This means that the Radius is 12.

The area of a circle is represented as;

\(Area = \pi(radius)^2\)

We have the requirements to find the area, with the value of the radius.

Solve for the area;

\(Area = \pi(12)^2\)

\(Area = 144 \pi\) (Exact)

\(Area = about \ 452.39.\) (Approx.)

Answer:

68 %

Step-by-step explanation:

The Empirical rule formula states that:

• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

Mean of 96 and a Standard deviation of 17

Applying , the first empirical rule for 1 standard deviation from the mean, we have:

μ - σ

96 - 17

= 79

μ + σ

96 + 17

= 113

Therefore, the percentage of IQ scores that are between 79 and 113 is 68%

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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Answer:

Output= -31

Step-by-step explanation:

f(x)= -3x²+8x-3

Therefore, f(-2)= -3(-2)²+8(-2)-3

                        = -3×4 -16 -3

                         = -12-16-3

                          = -31

Answer:

\(Fraction = \frac{1}{5}\)

Step-by-step explanation:

Given

\(Trays = 20\)

\(Each\ Tray = 5\ colors\)

\(Each\ set = 1\ Purple\)

Required

Fraction of purple in 20 trays

If there are 20 trays, then the total colors is:

\(Colors= 20 * 5\)

\(Colors= 100\)

This also means that, there are 20 purple colors in the set (i.e. 20 trays * 1 purple)

So, the fraction of purple color is:

\(Fraction = \frac{Purple}{Total}\)

\(Fraction = \frac{20}{100}\)

\(Fraction = \frac{1}{5}\)

Dish D has the density of clusters closest to 0.75 per square centimeter.

A substance's density is determined by how much mass there is per unit volume. It is typically expressed in units such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).

To find the density of clusters in each circular dish, we need to calculate the area of each dish and divide the number of clusters by that area.

The area of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, we are given the diameter of each circular dish, which is 8 cm. Therefore, the radius of each dish is 4 cm.

The area of each dish is:

A = πr² = π(4 cm)² ≈ 50.27 cm²

Now, we can calculate the density of clusters in each dish:

Density in A = 53 clusters / 50.27 cm² ≈ 1.05 clusters/cm²

Density in B = 13 clusters / 50.27 cm² ≈ 0.26 clusters/cm²

Density in C = 151 clusters / 50.27 cm² ≈ 3.00 clusters/cm²

Density in D = 38 clusters / 50.27 cm² ≈ 0.76 clusters/cm²

Therefore, dish D has the density of clusters closest to 0.75 per square centimeter.

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Answer:

P(A) ∪ P(B) ⊆ P(A ∪ B) can be proved when \(X\) ∈ P ( A U B )

Step-by-step explanation:

To  Prove that P(A) ∪ P(B) ⊆ P(A ∪ B) is attached below and also a counter example to prove that we do not always get an equality is attached below as well

Hey there! :)

Answer:

Point V.

Step-by-step explanation:

Given the coordinates of T at (-6.5, 1), U represents T before any reflections. (Helps to visualize this better)

Reflecting across the x-axis results in the sign of the y-coordinate changed. Point T after this reflection becomes (-6.5, -1).

Finally, reflecting across the y-axis will change the sign for the x-coordinate.

(-6.5, -1) becomes (6.5, 1). This is represented by point V.

... None?

Not A because y = 2 is shown as forever 2 so cannot go through both points.

Not B because y = -x cannot go through (5,-2)

Not C because y = -2 cannot go through (0,0)

Not D because y = x cannot go through (5,2)

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

Answer: y=-5/3x+20 or y=-1 2/3x+20, so 20.

Step-by-step explanation: Actually, neither one of those options are correct. You may recall that the slope of the perpendicular line would be the exact opposite, the reciprocal, of the given line. The exact opposite of 3/5x is -5/3x, which could be reduced to -1.5x. From there, you could substitute x and y, which are 15 and -5 in this case, into the y=mx+b equation:

-5=-5/3(15)+b                            *b is y-intercept*

-5=-25+b                                   Multiplied -5/3 by 15 first

-20=b                                         Subtracted -25 from both sides (it'd be --25, so            

                                                  basically just +25)

20=b                                           Reciprocate b because you need the opposite

Hope this helps,

Lacia :))

You have the correct sequence of reasons

Here's what the full step by step picture looks like

3.25(1.25x + 0.5) = 10.5  ................ given

4.0625x +  1.625 = 10.5  ................ distributive property

4.0625x = 8.875  ................ subtraction property of equality

x = 2.18461538461539 ....... division property of equality

---------------------------

Notes:

Answer:

I am pretty sure that is right

Step-by-step explanation:

\(3.25(1.25+0.5) = 10.5\)   is given

Then you distribute the \(3.25\\\) to the \(1.25x\) and the \(0.5\).

\(3.25(1.25x)=4.06x\)

\(3.25(0.5)=1.6\)

So the new equation would be \(4.06x + 1.6= 10.5\)

Then you would subtract \(1.6\) from each side to get \(4.06x=8.9\)

Finally you would divide each side by \(4.06\) to get \(x= 1.93\).

Answer:

1) if b = 5

Answer: never a repeating decimal.

2) if b = 6

Answer: sometimes a repeating decimal

3) if b = 7

Answer: Always a repeating decimal

4) if b = 8

Answer: Sometimes a repeating decimal

5) if b = 9

Answer: Always a reapeating decimal.

Step-by-step explanation:

1) if b = 5

Answer: never a repeating decimal.

2) if b = 6

Answer: sometimes a repeating decimal

3) if b = 7

Answer: Always a repeating decimal

4) if b = 8

Answer: Sometimes a repeating decimal

5) if b = 9

Answer: Always a reapeating decimal.

Answer:

See below

Step-by-step explanation:

\(1) \: \frac{1}{2} \times 5 \times 6 = 15 \: {cm}^{2} \\ \\ 2) \: \frac{1}{2} \times 10 \times 6 = 30 \: {cm}^{2} \\ \\ 3) \: 5 \times 3 = 15 \: {cm}^{2} \\ \\ 4) \: 10 \times 6= 60\: {cm}^{2} \)

The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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The value of y is 6 and the length of RS and ST are 28, 26 respectively.

What is a line ?

line is a straight one dimensional figure having no thickness is called as the line.

Given , number lines

RS = 4y+4

ST = 3y+8

RT = 54

From the given figure ,

RS+ST = RT

4y+4+3y+8 = 54

7y+12 = 54

7y = 54-12

7y = 42

y =42/7

y = 6

The RS = 4y+4 = 4*6+4 = 28

ST = 3y+8 = 3*6+8 = 26

Hence, The value of y is 6 and the length of RS and ST are 28, 26 respectively.

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Answer:

See below for proof

Step-by-step explanation:

\(\displaystyle \frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{(1-\cos x)(1+\cos x)}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{1-\cos^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{\sin x(1+\cos x)}{\sin^2 x}\\\\\frac{\sin x}{1-\cos x}=\frac{1+\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\frac{1}{\sin x}+\frac{\cos x}{\sin x}\\\\\frac{\sin x}{1-\cos x}=\csc x+\cot x\)

Answer:

C(x)=0.65x+8

Step-by-step explanation:

According to the information given, you can say that the total cost would be equal to the result of multiplying the cost of the meat and bun per burger for the number of burgers made plus the amount spent on condiments and supplies, which can be expressed as:

C(x)=0.65x+8, where:

C(x) is the total cost

x is the number of burgers made

Answer:

5/9 of the marbles are red

Step-by-step explanation:

Of the 45 marbles, 20 are black, and the other 25 are red. So 25/45, or 5/9, of the marbles are red.

9514 1404 393

Answer:

  PQ = 46

Step-by-step explanation:

Midsegment ST is half the length of base segment PQ.

  2×ST = PQ

  2×(5x -22) = 3x +19

  10x -44 = 3x +19 . . . . . . . eliminate parentheses

  7x = 63 . . . . . . . . . . . . add 44-3x

  x = 9 . . . . . . . . . . . . divide by 7

PQ = 3x +19 = 3×9 +19

PQ = 46

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

angle 7= 66

Step-by-step explanation:

Angle 1 is equal to the 114 degrees. And angle 1 + angle 7 = 180. So it would be 114 + angle 7 = 180. So you do 180-114 = 66. So angle 7= 66.

The other way is that 114 + angle 6 = 180, so you do 180-114= 66.

And agle 6 is equal to angle 7, so that's another way you can know that angle 7= 66

The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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The total number of yards the friends who paddle the Adventure Mid travel is 8,580 yards

Number of friends who paddle Adventure Mid Trip = 40% of 15

= 0.4 × 15

= 6 friends

Total yards the friends who paddle the Adventure Mid Trip travel = Total length of travel

= 4 7/8 miles

Recall,

1 mile = 1760 yards

Total yards the friends who paddle the Adventure = 4 7/8 × 1,760

= 39/8 × 1,760

= (39 × 1,760) / 8

= 68,640 / 8

= 8,580 yards

Consequently, the task content is solved by converting number of miles to yards.

Complete question:

Great Adventures Canoe and Kayak company offers 3 different options as shown in the table. This afternoon a group of 15 friends paddle the different options in individual kayaks and 40% of the group paddle the Adventure Mid Trip. How many total yards will the friends who paddle the Adventure Mid Trip travel? (Hint: 1 mile = 1760 yards)

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Answer:

10x+6

Step-by-step explanation:

you would times the 2 by the 5 and the 2 by the 3 which gives you 10x+6

Simon will receive R13,342.80, Thato will receive R29,649.60, and Elton will receive R19,167.60 after dividing the money from the Stokvel.

To calculate the amount of money that was invested in the Stokvel, we need to sum up the individual contributions of Simon, Thato, and Elton. Adding their contributions:

R9,000 + R20,000 + R13,000 = R42,000.

Therefore, R42,000 was invested in the Stokvel.

To calculate the amount of money that will be there in the investment after 5 years, we can apply the effective growth rate of 48% to the initial investment of R42,000.

Amount after 5 years = R42,000 + (48/100) \(\times\) R42,000 = R42,000 + R20,160 = R62,160.

After 5 years, there will be R62,160 in investment.

To calculate how much money each member will receive if they decide to withdraw and divide the whole money in the ratio of their initial contributions, we need to find the proportion of the total amount that each member contributed.

Simon's share = (R9,000 / R42,000) \(\times\) R62,160,

Thato's share = (R20,000 / R42,000) \(\times\) R62,160,

Elton's share = (R13,000 / R42,000) \(\times\) R62,160.

Calculating each share:

Simon's share = (0.2143) \(\times\)R62,160 = R13,342.80,

Thato's share = (0.4762) \(\times\)R62,160 = R29,649.60,

Elton's share = (0.3095) \(\times\)R62,160 = R19,167.60.

Therefore, Simon will receive R13,342.80, Thato will receive R29,649.60, and Elton will receive R19,167.60 after dividing the money from the Stokvel.

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Answer:

3

Step-by-step explanation

Q and R are already given to you so you just have to look

Given the angle bisectors of ΔPQR are PZ, QZ, and RZ, note that:

In geometry, an angle bisector is a line that divides an angle into two equal angles. A bisector is anything that divides a form or item into two equal pieces.

An angle bisector is a ray that divides an angle into two equal portions of the same measurement.

The computation is explained as follows;

Since m∠YRZ = 14° (given)

Note that on the bases of the Angle Bisector theorem,

m∠YRZ = m∠XRZ = 1/2 m∠YRX

Since

∠YRZ = 14°

m∠YRX = 2 * 14°  = 28°

Recall that ∠WPY is 46°, and m∠YRX = 28°

Thus, m∠PQR = 180 - (28 + 46)

∠PQR = 106°

Given the above, m∠XQZ = ∠PQR * 1/2

∠XQZ  =  106/2

∠XQZ  =  53°

Since Z is the center of the ΔPQR, Z is equidistant from the three edges so:

WZ = YZ = XZ

WZ = 14,

Thus, XZ = 14

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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As a result, z = 30 is the equation of line B, which is perpendicular to line C and passes through the point (30, -10). The response is (E).

A mathematical assertion that shows the equality between two expressions is called an equation. It has two sides, each divided by an equal sign. The terms on each side of the equal sign generally contain variables, constants, and mathematical operations including addition, subtraction, multiplication, division, exponents, and roots. For instance, the expressions 2x + 3 and 7 are identical when the equation 2x + 3 = 7 is used. By applying inverse operations to both sides of the equation, it is possible to solve this equation for the variable x, leading to the result x = 2.

given

We must first determine the slope of line C in order to determine the equation of line B, which intersects line C at the point (30, -10) and is perpendicular to it; its equation is y - 5 = 10.

The equation for line C can be rewritten as y = 15, which is of the form y = mx + b, where m denotes the slope and b the y-intercept.

As y is constant and does not change while x changes in this situation, line C has a slope of 0.

Line B's slope is equal to the negative reciprocal of line C's slope because it is perpendicular to line C.

As line C has a slope of 0, line B's slope is unknown (since it is a vertical line).

As a result, z = 30 is the equation of line B, which is perpendicular to line C and passes through the point (30, -10). The response is (E).

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