use mental math to complete the pattern(5×6^3=5__6__? Can you help me with the two blank spaces

Answer: (1/6)^2

Step-by-step explanation:

Answer:

The third answer is correct

Step-by-step explanation:

Use the properties of degrees:

1)

\( {( \frac{1}{108} })^{3} = \frac{ {1}^{3} }{ {108}^{3} } = \frac{1}{6561} \)

\( \frac{1}{6561} ≠ \frac{1}{36} \)

.

2)

\( ({ \frac{1}{9} })^{3} = \frac{ {1}^{3} }{ {9}^{3} } = \frac{1}{729} \)

\( \frac{1}{729} ≠ \frac{1}{36} \)

.

3)

\( ({ \frac{1}{6} })^{2} = \frac{ {1}^{2} }{ {6}^{2} } = \frac{1}{36} \)

\( \frac{1}{36} = \frac{1}{36} \)

The scale factor between a square of dimensions 7 by 7 and a scaled copy of dimensions 21/2 by 21/2 is 3/2 or 1.5.

We know that the dimensions of the square on the left are 7 by 7, and the dimensions of the square on the right are 21/2 by 21/2.

To find the scale factor, we can divide the dimensions of the square on the right by the dimensions of the square on the left

scale factor = (21/2) / 7

We can simplify this fraction by dividing both the numerator and the denominator by the greatest common factor, which is 7

scale factor = (21/2) / 7 = (21/2) * (1/7) = 3/2

Therefore, the scale factor is 3/2, or 1.5.

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That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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Answer:

p=q^3

Step-by-step explanation:

The formula for p  in terms of q is p = 0.4 q³

Direct Proportion means when one variable changes the other also changes in the same direction by some proportion.

It is given that

p ∝ q³

p = k q³

here k is the proportionality constant

It is also given that when q = 15 , p = 1350

1350 = k * 15³

k = 0.4

Therefore

The formula for p  in terms of q is

p = 0.4 q³

The complete question is

p is directly proportional to the cube of q . When , q = 15 , p = 1350

Find a formula for p  in terms of q

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Answer: part A is 1 and part B is 14

Step-by-step explanation:

====================================

Answer:

\( \boxed{\sf 3f(x) + 2g(x)= 3 {x}^{2} + 3 x - 8} \)

Given:

f(x) = x² - 4

g(x) = 3x + 2

To Find:

\( \sf 3f(x) + 2g(x)\)

Step-by-step explanation:

\(\sf \implies 3f(x) + 2g(x) \\ \\ \sf \implies 3( {x}^{2} - 4) + 2(3x + 2) \\ \\ \sf \implies (3 \times {x}^{2} ) - (3 \times 4) + (2 \times 3x) + (2 \times 2) \\ \\ \sf \implies 3 {x}^{2} - 12 + 3x + 4 \\ \\ \sf \implies 3 {x}^{2} + 3x + ( - 12 + 4) \\ \\ \sf \implies 3 {x}^{2} + 3 x - 8\)

Based on the given information and measurements, the following statements are true:

The perimeter of the full-size game board is six times the perimeter of the travel-edition game board: This statement is false. The perimeter of the full-size game board can be calculated as the sum of the lengths of its three sides: AB + BC + AC = 32 + 52 + 52 = 136 cm. The perimeter of the travel-edition game board can be calculated as the sum of the lengths of its three sides: AX + XY + YZ = 13 + 21 + 18 = 52 cm. Therefore, the perimeter of the full-size game board is 2.62 times the perimeter of the travel-edition game board, not 6 times.

The travel-edition side corresponding to the 48-cm side on the full-size board will measure 12 centimeters: This statement is false. The travel-edition side corresponding to the 48-cm side on the full-size board is side XY. The length of XY can be calculated using proportions: XY/48 = YZ/52, which gives XY = 48*18/52 = 16.62 cm (rounded to two decimal places).

The travel-edition side corresponding to the 48-cm side on the travel-edition board will measure 13 centimeters: This statement is true. The travel-edition side corresponding to the 48-cm side on the travel-edition board is side AX, which has a length of 13 cm.

The three angles represented on the travel-edition board are congruent to their corresponding angles on the full-size board: This statement is true. The three angles of a triangle are determined by the lengths of its sides, so if two triangles have the same side lengths, their angles must be congruent as well.

Therefore, the three angles represented on the travel-edition board (at vertices A, X, and Y) are congruent to their corresponding angles on the full-size board (at vertices A, B, and C).

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If we move 8 units right and end up at the coordinate (5,-3) the starting point is (-3,-3)

In an x-y plane, the x-axis is the axis along the horizontal of the plane. Similarly, the y-axis is the axis along the vertical of the plane.

Thus, the change in the position affects the coordinates of the x and y axis accordingly.

Given:

Change in position: 8 unit rights

Thus, the movement is along the x-axis in the positive direction

Final position: (5,-3)

Starting point can be found by subtracting the movement of the particle from the endpoint.

Thus, Starting position: (5-8,-3) or (-3,-3)

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Rounding to the nearest whole number. The correct option is D) 216 m²; 244 m².

Since the prism has a rectangular base, we know that its lateral faces are all rectangles with heights equal to the height of the prism. Let's first find the lateral area of the prism using the formula:

Lateral Area = Perimeter of Base * Height

The perimeter of the base is the sum of the lengths of all four sides of the rectangle. Since there are two bases, we will add their perimeters together. The length and width of each base are 12 m and 7 m, respectively, so:

Perimeter of Base = 2 * (Length + Width) = 2 * (12 + 7) = 38 m

The height of the prism is given as 10 m, so:

Lateral Area = 38 * 10 = 380 m²

Next, we need to find the surface area of the prism. This consists of the lateral area we just found, plus the areas of the two bases. Each base has an area of 12 * 7 = 84 m², so:

Surface Area = 2 * Base Area + Lateral Area = 2 * 84 + 380 = 548 m²

Rounding to the nearest whole number, we get:

Lateral Area ≈ 380 m²

Surface Area ≈ 548 m²

Therefore, the answer is option D) 216 m²; 244 m².

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The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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The area of a rectangle is given by the formula:

Area = length x width

In this case, the length of the park is x + 5 and the width is x - 2. So, we can substitute these expressions into the formula to get:

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

Expanding the product, we get:

Area = x^2 + 5x - 2x - 10

Simplifying, we have:

Area = x^2 + 3x - 10

Therefore, the area of the rectangular park is given by the expression x^2 + 3x - 10.

Answer:

n/ ( y^2+x) = c

Step-by-step explanation:

n - cx = cy^2

Add cx to each side

n -cx+cx = cy^2 +cx

n = cy^2 +cx

Factor out c

n = c( y^2 +x)

Divide each side by y^2 +x

n/ ( y^2+x) = c  ( y^2 +x)/ ( y^2 +x)

n/ ( y^2+x) = c

Step-by-step explanation:

\( \frac{1 + \cot(x) }{ \cos(x) } - \csc(x) = \sec(x) \)

\( \frac{1}{ \cos(x) } + \frac{ \cot(x) }{ \cos(x) } - \csc(x) = \sec(x) \)

\( \sec(x) + \frac{1}{ \sin(x) } - \csc(x) = \sec(x) \)

\( \sec(x) + \csc(x) - \csc(x) = \sec(x) \)

\( \sec(x) = \sec(x) \)

Answer:

To find 29% of 150, we can first express 29% as a decimal by dividing 29 by 100. 29% is the same as 0.29.

Then, we multiply 0.29 by 150 to find the answer:

0.29 * 150 = 43.5

So, 29% of 150 is equal to 43.5.

Here's the work:

29% * 150 = 0.29 * 150 = 43.5

\(\huge\text{Hey there!}\)

\(\mathsf{29\%\ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \ of \ 150}\)

\(\mathsf{= \dfrac{29}{100} \times 150}\)

\(\mathsf{= \dfrac{29}{100} \times \dfrac{150}{1}}\)

\(\mathsf{= \dfrac{29(150)}{100(1)}}\)

\(\mathsf{= \dfrac{4,350}{100}}\)

\(\mathsf{= \dfrac{4,350 \div 50}{100 \div 50}}\)

\(\mathsf{= \dfrac{87}{2}}\)

\(\mathsf{= 43 \dfrac{1}{2}}\)

\(\mathsf{= 43.5}\)

\(\huge\text{Therefore, your answer should be:}\)

\(\huge\boxed{\mathsf{\dfrac{87}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43 \dfrac{1}{2}}}\huge\checkmark\)

\(\huge\boxed{\mathsf{43.5}}\huge\checkmark\)

\(\large\text{Either of those should work because they are all equivalent to each}\\\large\text{other}\uparrow\)

\(\huge\text{Good luck on your assignment \& enjoy your day! }\)

The ratio shows how many times one value is contained in another value.

The number of top dogs is 192.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of top dogs to fat cats was 24 to 19.

if they were 152 fat cats.

This means,

Number of top dogs = 24x

Number of fat cats = 19x

Now,

Number of fat cats = 152

This means,

152 = 19x

x = 8

Now,

Number of top dogs = 24x

= 24x

= 24 x 8

= 192

Thus,

The number of top dogs is 192.

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Answer: 142825

Step-by-step explanation:

If \(t\) is the number of years, then the population is \(P(t)=100000(1.02)^t\).

Setting \(t=18\). \(P(18)=100000(1.02)^{18} \approx 142825\).

Answer:

  14 donuts

Step-by-step explanation:

Packing circles in a rectangular space is always an interesting problem. Sometimes, it works well to put them on a grid. Other times, more circles can be packed in if they are somewhat off-grid. The details depend on the specific dimensions.

The attached shows a way to fit 14 donuts in the box.

_____

Additional comment

Packing them on a square grid allows only 12 donuts to be put in the box.

Answer:

10:4

35:14

55:22

Answer:

∠A= ∠E, ∠H = ∠D

and the last one

Step-by-step explanation:

opposite angles are equal, alternative interior angle are equal.

Answer:

∠A = ∠E and ∠H = ∠D.

∠E = ∠H and ∠F = ∠G

Step-by-step explanation:

Angles A and E are one set of corresponding angles and angles H and D are another set.  Corresponding angles are always congruent to each other and thus equal. Therefore, ∠A = ∠E and ∠H = ∠D.

Angles E and H are one set of vertical angles and angles F and G are another set.  Vertical angles are also always congruent to each other and thus equal.  Therefore ∠E = ∠H and ∠F = ∠G

Answer:

Step-by-step explanation:

What are the other colors?

if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2

similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....

depends on how many colors are there

Answer:

d. Several means when there are two independent variables, and the same entities have been used in all conditions.

Step-by-step explanation:

ANOVA is an abbreviation for analysis of variance and it was developed by the notable statistician Ronald Fisher. It is typically a collection of statistical models with their respective estimation procedures used for the analysis of the difference between the group of means found in a sample. Simply stated, ANOVA helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors. In Statistics, the random factors doesn't have any significant impact on the data set but the systematic factors does have an influence.

Two-way repeated-measures ANOVA compares several means when there are two independent variables, and the same entities have been used in all conditions.

Hence, the aim of a two-way analysis of variance (ANOVA) is to give the relationship or identify if there is an interaction between the two independent variables on the dependent variable.

Answer:

25 sheets

Step-by-step explanation:

=42-17 = 25 sheets

Answer:

25 sheets of paper

Step-by-step explanation:

42-17=25

Answer:

583.3

Step-by-step explanation:

Answer:

4.21x10^9

Step-by-step explanation:

The exponent is positive because the number is large.:-)

Answer:

Step-by-step explanation:

Percentage of girls = 35%

Percentage of boys = 100 - 35 = 65%

There are 910 boys:

65% = 910

Find the number of students in the school:

1% = 910 ÷ 65 = 14

100% = 14 x 100 = 1400

Answer: There are 1400 students in the school

The marginal cost of producing the next unit of output always affects the average total cost, so the marginal cost curve always intersects the average total cost curve at its lowest point.

The difference in overall production costs caused by creating or producing one more unit is known as the marginal cost.

By producing at the point where marginal cost (MC) equals marginal revenue, a business can optimize its earnings (MR).

Because fixed costs are fixed regardless of output levels, larger production spreads the total fixed cost over more units, resulting in a lower fixed cost per unit.

Production levels affect variable costs, so increasing the number of units will increase those costs.

Companies need to be aware of the situations when expanding production entails step costs as a result of shifting relevant ranges.

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Answer:

156 cm³

Step-by-step explanation:

The solid is a prism with a trapezoid base.

volume = (area of base) × height

V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm

V = 156 cm³

The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

Answer:

Answer:

Step-by-step explanation:

(a) A = 23°

(b) A=99°

(c) A = 53°

(d) A= 36°