A rocking horse has a weight limit of 60 pounds.

What percentage of the weight limit is 33 pounds?
What percentage of the weight limit is 114 pounds?
What weight is 95% of the limit?

Answer:

circumference = 131.9

area = 1385

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

Circumference of a circle: 2πr

π = 22/7

r = d/2

r = 42/2

r = 21

2 × 21 × 22/7

42 × 22/7 = 924 ÷ 7 = 132

Circumference = 132m

Area of the circle: πr²

π = 22/7

r = 21

22/7 × (21²)

22/7 × 441 = 9702 ÷ 7 = 1386

Area = 1386 m²

Hope this helps!

Answer:

y = -2x + 4

Step-by-step explanation:

First, find the slope by doing rise over run. I did this between the points (0, 4) and (2,0) This gives you -4/2 = -2.

Then, find the y-intercept, which is where the line goes through the y axis. This is at y = 4.

So, the equation is y = -2x + 4.

Answer:

y = -2x + 4

Step-by-step explanation:

Lets write the equation of the line in slope-intercept form. We need to find two things:

1) the y-intercept. When can find this by simply finding what y is equal to when x is 0. Taking a quick look, we can find that it is 4

2) the slope. To find the slope, we simply take the rate of change, or rise over run. Taking the section where x is between 0 and 2, we have, 4/2 = 2.

However, the line is moving downwards, so its a negative slope. This means the actual slope is -2.

Finally, slope-intercept form tells us that the line is y = mx + b, where m is the slope, and b is the y-intercept.

Therefore, the answer is:

y = -2x + 4

Answer:

Step-by-step explanation:

5

Statement. (Reasons are in boldfaced words)

1. H is the midpoint of AD. By given.

2. AD bisects GC. By given.

3. HA = HD. By definition of midpoint.

4. GH = CH. By definition of the bisector.

5. Angles AHG and DHC are congruent. By vertical angles theorem.

6. AG = DC. They are the height of the figure.

7. Triangles GHA and CHD are congruent. By Side-Angle-Side postulate of congruence.

The expression cos (125°) - cos 55° cos 35° cos 55° can be written as cos (55°) + cos (55°) cos (35°) cos (55°).

cos (125°) can be rewritten as cos (180° - 125°). Similarly, cos (35°) can be rewritten as cos (180° - 35°). Therefore, the expression can be written as:

cos (180° - 125°) - cos (55°) cos (180° - 35°) cos (55°)

Simplifying further, we have:

cos (55°) - cos (55°) cos (145°) cos (55°)

Since 145° is the supplement of 35°, we can rewrite it as:

cos (55°) - cos (55°) cos (180° - 35°) cos (55°)

Now, cos (180° - 35°) is equal to -cos (35°). Therefore, the expression becomes:

cos (55°) + cos (55°) cos (35°) cos (55°)

Hence, the expression as a function of an acute angle is:

cos (55°) + cos (55°) cos (35°) cos (55°)

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The best estimate for a kitchen sink is 20 liters from the options given.

Option C is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The average capacity of a kitchen sink = 32 liters.

The best estimate for the capacity of a kitchen sink.

= 20 liters to 40 liters

Thus,

20 liters can be our best estimate.

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The equation y = x - 0.3x represents a situation in which the price of a product decreases by 30% due to a discount.What does the equation y = x - 0.3x represent.

The equation y = x - 0.3x can be simplified as y = 0.7x, where x represents the original price and y represents the new price after the discount of 30%.This equation can be used to calculate the new price of a product after a discount of 30% has been applied.A case where a product's price drops by 30% as a result of a discount is depicted by the equation y = x - 0.3x.What the expression y = x - 0.3x means.The formula y = x - 0.3x may be condensed to y = 0.7x, where x stands for the original price and y for the new price following the 30% discount.This formula may be used to determine a product's new pricing after a 30% discount has been applied.

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in a parcel described as the SW ¼ of the NE ¼ of the SE ¼ the correct answer is option D 10.

To determine the number of acres in a parcel described as the SW ¼ of the NE ¼ of the SE ¼, we need to multiply the acreage of each quarter section.

Starting with the SE ¼, we know that a quarter section (1/4) consists of 160 acres. Therefore, the SE ¼ is 160 acres.

Moving to the NE ¼ of the SE ¼, we need to calculate 1/4 of the 160 acres. 1/4 of 160 acres is (1/4) * 160 = 40 acres.

Finally, we consider the SW ¼ of the NE ¼ of the SE ¼. Again, we need to calculate 1/4 of the 40 acres. 1/4 of 40 acres is (1/4) * 40 = 10 acres.

Therefore, the parcel described as the SW ¼ of the NE ¼ of the SE ¼ consists of 10 acres.

Hence, the correct answer is option D) 10.

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Answer:

SSS, SAS, AAS, or ASA.

Step-by-step explanation:

SSS refers to all three sides being congruent with the two triangles you're comparing.

SAS refers to one angle between two congruent sides with the two triangles you're comparing.

AAS refers to one angle and one side between an angle with the two triangles you're comparing.

ASA refers to two congruent angles between a side with the two triangles you're comparing.

Definition VS Theorem

Definition: In order for two triangles to be classified as "similar" triangles, each triangle's angles must be congruent with the corresponding angle of the other triangle, and each of their three corresponding side pairs must all form a common ratio.

Theorems: Proving just some of those 6 parts is sufficient to prove triangle Similarity, specifically: SSS, SAS, or AA

In order for two triangles to be classified as "similar" triangles, their corresponding angles must be congruent, and their corresponding side pairs must all form a common ratio.

This means that to prove \(\triangle A_1B_1C_1\) is similar to \(\triangle A_2B_2C_2\), we'd need to prove

\(\angle A_1 \cong \angle A_2\),

\(\angle B_1 \cong \angle B_2\), and

\(\angle C_1 \cong \angle C_2\),

as well as prove that there exists a single positive number "k" such that the following equation is true for the ratios of corresponding side lengths:

\(\dfrac{A_1B_1}{A_2B_2}=\dfrac{B_1C_1}{B_2C_2}=\dfrac{A_1C_1}{A_2C_2}=k\)

Fortunately, instead of finding all of those quantities, and proving all 6 of those things true, there are several theorems that allow us to prove less than all 6 of those things, yet still be sufficient to prove that the triangles are similar.

Note that if two Triangles are Congruent, then they are Similar.  It is a special case of Similar Triangles where k=1.

To deal with all of the triangles that are Similar but not Congruent, there are three cases where triangle must be Similar:

SSS (Side-Side-Side)

SAS  (Side-Angle-Side)

AA (Angle-Angle)

WARNING:  Even though SSS looks just like SSS for Triangle congruence, Similarity, is different than congruence.  We're doing a different thing for similarity.  For these three Similarity rules, angles must be proven congruent, and corresponding sides must form a ratio that is common to all of the other corresponding side ratios for the theorem.

SSS (Side-Side-Side)

If all three corresponding side pairs form a common ratio, that's enough.  It will force the corresponding angles to be congruent.

SAS (Side-Angle-Side)

Here, if two corresponding side pairs form a common ratio, AND if the corresponding angles between those two sides on each triangle are congruent, then the two triangles must be Similar.

AA (Angle-Angle)

Here, if just any two corresponding angle pairs are congruent, then the two triangles must be Similar.  This is enough to force the third angle pair to be congruent, and all of the corresponding side pairs to have a common ratio.

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \begin{array}{llll} \textit{\tiny "y" varies directly}\\ \textit{\tiny with the square of "x" } \end{array}}{y = kx^2}\qquad \textit{we also know that} \begin{cases} x = 8\\ y = 32 \end{cases} \\\\\\ 32=k(8)^2\implies \cfrac{32}{8^2}=k\implies \cfrac{1}{2}=k~\hfill \boxed{y=\cfrac{1}{2}x^2} \\\\\\ \textit{when y = 112.5, what is "x"?}\qquad 112.5=\cfrac{1}{2}x^2 \\\\\\ 225=x^2\implies \sqrt{225}=x\implies 15=x\)

Answer:

a 3 pound almonds is the best deal with the 5 pound bag of walnuts being the second and the 4 pounds of cashews is the worst deal

Step-by-step explanation:

the almonds cost 5.50$ a pound the 5 pound bag of walnuts cost 5.75$ dollars a pound and the 4 pound bag of cashews cost  6.20$ a pound    

(-2, 3) are the coordinates of point D of parallelogram.

A(-7,1), B(-3, -6), C(2, -4)

Let the 4th point D = (x , y)

In a parallelogram, diagonals bisect each other.

midpoint of BD = midpoint of AC

If two points are (x₁ , y₁) and (x₂,y₂)

then midpoint = {(x₁+x₂)/2 , (y₁+y₂)/2}

midpoint of AC = {(-7 + 2)/2 , (1-4)/2}

= {-5/2 , -3/2}

midpoint of BD = {(-3 + x)/2 , (-6 + y)/2}

Now,

midpoint of BD = midpoint of AC

{-5/2 , -3/2} =  {(-3 + x)/2 , (-6 + y)/2}

Comparing both sides

(-3 + x)/2 = -5/2

-3+x=-5

x=-2

taking y -coordinate

(-6+ y)/2 = -3/2

-6 + y = -3

y = 3

Point D (x , y) = (-2, 3)

Hence,  (-2, 3) are the coordinates of point D of parallelogram.

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Answer:

700

Step-by-step explanation:

Please give brainliest

Divide 1750 by 5 and get 350.

350 times 2 is 700

Answer: \(x=2\)

Step-by-step explanation:

Let's solve your equation step-by step

\(3(4-2x)=x-2\)

First we need to use the distributive property

\((3)(4)-(3)(2x)=x-2\\-6x+12=x-2\)

Now let's subtract x from both sides

\(-6x+12-x=x-2-x\\-7x+12=-2\)

Next let's subtract 12 from both sides

\(-7x+12-12=-2-12\\-7x=-14\)

Finally divide both sides by -7

\(\frac{-7x}{-7} =\frac{-14}{-7} \\x=2\)

Sample size and the confidence level width have an inverse relationship. As the sample size increases, the confidence level width decreases.

When determining a confidence interval for a population parameter, such as the mean or proportion, a larger sample size provides more information about the population. This increased information leads to a narrower confidence interval.

The confidence level width is influenced by two factors: the sample standard deviation (or the variability of the data) and the critical value associated with the desired confidence level. As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation. This reduces the variability and leads to a narrower confidence interval.

A larger sample size leads to a decrease in the confidence level width, providing a more precise estimate of the population parameter with a higher level of confidence.

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Answer:

Solution given:fig 1

base[b]=4cm

height[h]=15cm

we have

Area of parallelogram=b×h=15×4=60cm²

Solution given:fig 2

base[b]=18cm

height[h]=3cm

we have

Area of parallelogram=b×h=18×3=54cm²

Step-by-step explanation:

Solution given:fig 3

base[b]=11cm

height[h]=6cm

we have

Area of parallelogram=b×h=11×6=66cm²

Solution given:fig 4

base[b]=12cm

height[h]=5cm

we have

Area of parallelogram=b×h=12×5=60cm²

So fig 1 =fig 4[Area]

Given:

Bird center bar chart is given.

Option D is the final answer.

Answer:

Answer: The scale factor of the triangle is 4

Step-by-step explanation:

Answer:

55

because 4x and 1 are alt exterior angles

Step-by-step explanatio

125+4x-5=180

4x-5=55

4x=60

x=15

4(15)-5

55= angle 1

Answer:

84.823 cm^3

Step-by-step explanation:

V=πr2h=π·32·3≈84.823

Answer:

V = 27 pi cm^3

Step-by-step explanation:

To find the volume, we use the formula

V = pi r^2 h

Where r is the radius and h is the height

We know the circumference is given by

C = 2 pi r

6 pi = 2 * pi * r

Solving for r

3 = r

Going back to V

V = pi * (3) ^2 * 3

V = 27 pi cm^3

Using the given expression and applying the law of indices, The step by step solution gives the final answer to be 42.13 .

A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.

The laws of indices, also known as the laws of exponents, are a set of rules that govern how exponents (or indices) are used in mathematical operations. These laws include:

These laws allow us to simplify expressions with exponents and make it easier to perform calculations involving them.

\(= 25 * \sqrt[401]2}^{302}\\= 25 * (2^{\frac {1}{401}})^{302}\\=25*2^{\frac {302}{401}}\\=25*2^{0.75}\\=42.13\\\)

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Use at least 3 decimals in your calculations in this question. A group of economists would like to study the gender wage gap, In a random sample of 350 male workers, the mean hourhy wage was 14.2, and the standard deviation was 2.2. In an independent random sample of 250 female workers, the mean hocirly wage was 13.3, and the standard devlation Was 1.4. 1. The cconomists would like to test the null hypothesis that the mean hourly wage of male and female workers are the same, against the aiternative hypothesis that the mean wages are different. Use the reiection region approach to conduct the hypothesis test, at the 5% significance level. Be sure to include the sample statistic; its sampling distribution; and the reason why the sampling distritution is valid as part of your answer. 2. Calculate the 95% confidence interval for the difference between the popiation means that can be used to test the researchers nuill hypothesis (stated above) 3. Calculate the p-value. If the significance level had been 1% (instead of 58 ). What would the conclusion of the fipothesis test have bect?

The value of x is given as follows:

x = 90.

The value of x is obtained applying the two secant segment theorem, which means that the following equation will hold true:

a(x + a) = b(b + c)

(a secant is a segment that crosses the circumference of the circle twice, and the product has to be equal for each).

Hence, replacing the values of a, b and c, we can obtain the value of x as follows:

11(11 + x) = 24.2(24.2 + 21.7)

121 + 11x = 1110.78

x = (1110.78 - 121)/11

x = 90.

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The sine and tangent functions are negative in the second and third quadrants, so the correct answer is A. sin θ = -4/9 and tan θ = 9/4.

Tangent function is an important trigonometric function which is denoted by the symbol tan. It is used to calculate the ratio between the opposite side and the adjacent side of a right-angled triangle.

Since cos θ < 0, then theta must lie in the second or third quadrant of the unit circle.

To verify this answer, we can use the inverse trigonometric functions to find theta given sin theta and cos theta.

Using the inverse cosine function, we can find that θ = -53.13 degrees. Then, using the inverse sine function, we can verify that sin θ = -4/9.

Finally, using the inverse tangent function, we can verify that tan θ = 9/4.

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Answer:

15/X

Step-by-step explanation:

a number divided by 15

15/X

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

x = 5/3

Step-by-step explanation:

Solve for x:

3 x + 5 = 10

Subtract 5 from both sides:

3 x + (5 - 5) = 10 - 5

5 - 5 = 0:

3 x = 10 - 5

10 - 5 = 5:

3 x = 5

Divide both sides of 3 x = 5 by 3:

(3 x)/3 = 5/3

3/3 = 1:

Answer:  x = 5/3

Step-by-step explanation:

To solve for x, make it the subject of the equation and simplify:

3x + 5 = 10      [subtract five from both sides]

     3x = 5        [divide both sides by three]

       x = ⁵/₃

Answer:

1) Please find attached the given plot and sketch of the points created with Microsoft Word

2) The correct option is;

A. AA Similarity Postulate

Step-by-step explanation:

1) Please find attached the given plot and sketch of the points created with Microsoft Word

2) The given parameters are;

The coordinates of the points are A(0, 0), B(1, 0), C(1, 2), D(2, 0) and E(2, 4)

Therefore, we have;

The length of segment AB = 1

The length of segment BC = 2

The length of segment AD = 2

The length of segment DE = 4

Therefore, we have;

∠ABC = ∠ADE = 90°

∠BAC = = artctan(2/1) = ∠DAE = artctan(4/2) = 63.435°

Therefore, ΔABC and ΔADE are similar by AA Similarity Postulate