establish the identity

The value of x in right angle whose hypotenuse is given 74 m  one angle is 90° and other angle given is 30° to the nearest tenth is approximately 37 meters.

The branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles is known as Trigonometry. It involves studying the properties of trigonometric functions, which are mathematical functions that relate the angles of a triangle to the ratios of its sides.

In this triangle, the height is opposite the 30° angle and the hypotenuse is the longest side of the triangle. We can use the trigonometric function sine to relate the height and the hypotenuse:

sin(30°) = x / 74

To solve for x, we can multiply both sides by 74 and simplify:

x = 74 sin(30°)

x ≈ 37 (to the nearest tenth)

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Answer: 28/5

Step-by-step explanation:

each toy had a mass of 4/5 kilograms .there are 7 toys.so the total mass is

7 times 4/5=28/5 kilograms

hope it helps

The angle that is congruent to ∠S after the given rotation transformation is: ∠M

A rotation is defined as a type of transformation whereby the object is rotated about a fixed point. The direction of the rotation can either be clockwise or anticlockwise.

Now, rotating a specific point that has the coordinates as (x, y) by 180° about the origin in either a clockwise or counterclockwise direction, will produce a new point that has the coordinates (−x,−y)

Thus, if Polygon KLMN is the image of polygon PQRS after a 180 degree rotation, then we can say that the new image formed will have ∠M congruent to ∠S

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The probability that the sample proportion of households spending more than $125 a week is less than 0.32 is 0.3850.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: A Food Marketing Institute found that 33% of households spend more than $125 a week on groceries. Assume the population proportion is 0.33 and a simple random sample of 349 households is selected from the population.

We have to find the probability that the sample proportion of households spending more than $125 a week is less than 0.32.

P(p < 0.32)

= P(Z < 0.32-0.33 0.33 * 0.67/189

= P(z < -0.29)

= 0.3850

Hence, the probability that the sample proportion of households spending more than $125 a week is less than 0.32 is 0.3850.

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a) Using the formula for finance charge, we can find the balance after one year:

charge = r*(balance-payments+purchases)

Here, r = 16.73% = 0.1673 (as a decimal), payments = $300 per month = $3,600 per year, and purchases = 0 (since Chloe is not making any new purchases).

Let's assume that x is the balance after one year. Then, we can write:

0.1673*(7316.48-3600) = x - 3600

Simplifying and solving for x, we get:

x = $6,830.58

So, the credit card balance (to the nearest dollar) after one year would be $6,831.

b) If Chloe increases her monthly payment to $350 per month, then her payments for the year would be $4,200. Using the same formula as above, we can find the balance after one year:

0.1673*(7316.48-4200) = x - 4200

Simplifying and solving for x, we get:

x = $5,774.99

So, the credit card balance (to the nearest dollar) after one year with a $350 monthly payment would be $5,775.

Answer:

the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent.  option (C) √(2x² + x) is equivalent to the original expression √(2x) * √(x+3) when x > 0.

Step-by-step explanation:

To simplify the expression √(2x) * √(x+3), we can use the property of radicals that says:

√(a) * √(b) = √(a * b)

So, we have:

√(2x) * √(x+3) = √(2x * (x+3))

Multiplying out the terms inside the radical, we get:

√(2x * (x+3)) = √(2x² + 6x)

Therefore, the expression √(2x) * √(x+3) is equivalent to the radical expression √(2x² + 6x) when x > 0.

So, the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent:

√(2x² + 6x) = √(2x² + x + 5x) = √(x * (2x + 5)) = √x * √(2x + 5)

Answer:

$3.47

Step-by-step explanation:

They are selling the container for $3.97 and it costs them $0.50 to make each. So that means they'll make a profit of $3.47.

1.0% is the percent error for his estimate .

What is percent error?

When compared to the actual value, the percent error is the difference between the estimated and actual values. The relative error is multiplied by 100 to calculate the % error, in other words. The difference between an estimated number and a precise value is measured in percent error.

the percent error = {exact error - approximate error} * 100%/exact error

                             = (9.9 - 10) * 100/9.9

                             = 0.1/9.9 * 100%

                             ≈ 1.0%

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The table of value for the given function is written and graphed below

The function s(x) = -0.7x^2 can be evaluated for different values of x to obtain corresponding values of s(x). We can create a table of values for s(x) by choosing a range of x-values and then plugging them into the equation and evaluating.

The table of values for the function s(x) = -0.72x^2 is

x s(x)

-5 -17.5

-4 -11.2

-3 -6.3

-2 -2.8

-1 -0.7

0 0

1 -0.7

2 -2.8

3 -6.3

4 -11.2

5 -17.5

We can use this value to plot a graph using a graphing calculator

Kindly find the attached graph below

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Answer: there

Step-by-step explanation:

exactly 1 solution

The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

The likelihood or chance that a specific occurrence or outcome will occur is quantified by probability. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. For instance, there are two equally likely outcomes (heads or tails), but only one of them is heads, hence the probability of flipping a fair coin and obtaining heads is 0.5 or 50%. By dividing the number of favorable outcomes by the total number of possible outcomes, one can calculate probability.

given

We can see that Nestor won a medal in 6 out of the 10 trials by counting the number of victories.

We can use the binomial distribution with parameters n=10 (number of trials) and p=0.79 to calculate the likelihood that this will occur (probability of success).

The following calculation can be used to determine the likelihood of at least 6 successes in 10 trials:

P(X>=6) = 1 - P(X<=5)

Using a calculator for the binomial distribution, we obtain:

P(X>=6) = 90.1%

The predicted likelihood that Nestor will win at least six of the upcoming races is therefore 90.1%, which is closest to the correct response of -1%.

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The radius of the circle is 36 centimeters.

A circle's circumference may be divided up into its arcs. Two endpoints and the curve connecting them serve as its definition. The size of the central angle that subtends an arc determines its length. The formula L = r, where L is the length of the arc, r is the radius of the circle, and is the measurement of the central angle in radians, yields the length of an arc in radians. Arcs of circles are utilised in geometry and trigonometry as well as in many other contexts, including creating circular objects and calculating angles.

The length of an arc of a circle is given by the formula:

L = rθ

Given, length of the arc is 32π centimeters and central angle = 8/9π.

Substituting the value we have:

32π = r(8/9π)

r = (32π)/(8/9π)

r = 36

Hence, the radius of the circle is 36 centimeters.

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The complete question is:

The probability that the student was NOT a female that got a “A” is given as follows:

p = 10/19.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability that the student was NOT a female that got a “A” is obtained as follows:

p = 20/38

p = 10/19.

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Apprοximately 31 mοving bοxes οn the flοοr οf the stοrage unit, given the dimensiοns οf the bοxes and the aisle.

In mathematics and geοmetry, dimensiοns refer tο the number οf cοοrdinates needed tο specify the lοcatiοn οf a pοint οr οbject in space.

Tο calculate the number οf mοving bοxes that can fit οn the flοοr οf the stοrage unit, we need tο first calculate the usable flοοr space by subtracting the width οf the aisle frοm the tοtal width οf the stοrage unit.

The usable floor space can be calculated as follows:

Usable floor space = 10 ft - 3 ft (aisle) = 7 ft

Next, we need to calculate how many boxes can fit in a row along the length and width of the usable floor space.

Along the length of the floor space, we can fit:

Number of boxes along length = 10 ft / 18 in = 20/3 boxes

Similarly, along the width of the floor space, we can fit:

Number of boxes along width = 7 ft / 18 in = 14/3 boxes

Since we can only stack the boxes one layer high, the total number of boxes that can fit on the floor of the storage unit can be calculated by multiplying the number of boxes along the length by the number of boxes along the width:

Total number of boxes = (20/3) x (14/3) = 280/9 ≈ 31

Therefore, we can fit approximately 31 moving boxes on the floor of the storage unit, given the dimensions of the boxes and the aisle.

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Answer:

14.3cm

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]a^{2}[/tex] + [tex]7^{2}[/tex] = [tex]10^{2}[/tex]

[tex]a^{2}[/tex] + 49 = 100  Subtract 49 from both sides

[tex]a^{2}[/tex] + 49 - 49 = 100 - 49

[tex]a^{2}[/tex] = 51

[tex]\sqrt{a^{2} }[/tex] = [tex]\sqrt{51}[/tex]

a = 7.14142842854  This is a rounded number.  This is an irrational number.  That means that it never repeats or terminates.  It is like [tex]\pi[/tex].

We just found the left side of the base of the triangle.  We need to double this to find FG.

7.14142842854 x 2 = 14.2828568571

Round this to 1 decimal place 14.3

Helping in the name of Jesus.

Answer: 14.28 cm

Step-by-step explanation:

So, 10 squared = 7 squared + X squared.

This can be simplified to: 100 = 49 + X squared.

Then, you subtract 49, and are left with 51 = X squared

Then, take the square root if 51, you get approx. 7.14 cm.
since this is an equilateral triangle, the answer will be the same for the second half of the base.
So, 7.14 x 2, 14.28 cm

Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

We can start by finding the cost of cherries per pound:

2 3/5 pounds = (2 × 5 + 3) / 5 = 13/5 pounds

Cost of 13/5 pounds of cherries = $5.25

Cost of 1 pound of cherries = $5.25 ÷ (13/5) = $2

Now we can find the cost of 5.5 pounds of cherries:

Cost of 5.5 pounds of cherries = $2 × 5.5 = $11

Therefore, Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

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The probability that 16 randomly selected batteries will have a runtime of less than 27 hours is 0.0228.

Probability is a branch of mathematics that deals with the study of random events or outcomes. It involves the analysis of the likelihood or chance of a particular event occurring, given certain conditions or assumptions. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

Probability theory is used to analyze and understand random phenomena such as games of chance, weather patterns, financial markets, and many other areas of study. The main tools of probability theory include probability distributions, random variables, and statistical inference.

Probability distributions are mathematical functions that describe the probabilities of different outcomes for a particular event or experiment. Random variables are variables that take on different values based on the outcome of a random event, and they are used to calculate probabilities for a range of different scenarios.

We can use the central limit theorem to approximate the distribution of the sample means, where n=16. The sample mean, X', will also be normally distributed with a mean of μ = 30 hours and a standard deviation of σ/√n = 6/√16 = 1.5 hours.

Now, we need to find the probability that the sample mean is less than 27 hours:

P(X' < 27) = P(z < (27-30)/1.5) [converting to standard normal distribution using z-score]

P(X' < 27) = P(z < -2)

Looking up the z-table, we can find that the probability of a standard normal random variable being less than -2 is approximately 0.0228.

Therefore, the probability that 16 randomly selected batteries will have a runtime of less than 27 hours is 0.0228.

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The fractions equivalent to 2/5 are 4/10, 6/15, 8/20. The correct option is B.

When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.

Hence, the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

The fractions equivalent to 2/5 are 4/10, 6/15, 8/20,.

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Which of the lists below includes all of the above expressions that are equivalent to 2/5?

I, 2/6

II,  4/10

III, 6/15

IV. 10/20

V. 4 / 12

VI 8/20

A. I, III, V, VI

B. III, VI

C. II, III, VI

D. II, III, IV, VI

The Space Shuttle Discovery traveled 22.3 million miles more distance than the Space Shuttle Atlantis.

What is distance ?

To find how many more miles the Space Shuttle Discovery traveled than the Space Shuttle Atlantis, we can subtract the distance traveled by Atlantis from the distance traveled by Discovery:

148.2 million miles - 125.9 million miles = 22.3 million miles

Therefore, the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

What is Space Shuttle ?

The Space Shuttle was a reusable spacecraft designed and operated by NASA (the National Aeronautics and Space Administration) to carry astronauts and cargo into space. It was in service from 1981 until 2011, when the final mission was completed.

The Space Shuttle consisted of several components, including the orbiter, which was the main spacecraft, and the two solid rocket boosters and external fuel tank that provided the initial propulsion during liftoff. The orbiter was designed to carry up to seven crew members and could be used to deploy satellites, conduct scientific experiments, and perform other tasks in space.

The Space Shuttle was unique in that it could land like an airplane, allowing it to be reused multiple times. After completing a mission, the orbiter would re-enter Earth's atmosphere and glide to a landing on a runway.

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Complete question is: The space shuttle discovery traveled 148.2 million miles during its mission. The space shuttle Atlantis traveled 125.9 million miles. the Space Shuttle Discovery traveled 22.3 million miles more than the Space Shuttle Atlantis.

One of the solutions for the given graph is (-5,-4).

What is a graph and how to plot the values?

In the given graph, a straight line intersects the parabola at two points i.e., (-5, -4) and (2, 0).

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The period, phase shift, and cosine function of the graph are;

The period = π

The phase shift = π/8

The cosine function is; y = 2·cos(2·(x - π/8)) - 1

The period of the graph is the distance between two consecutive peaks of the wave.

The maximum value of the graph is 1 at x = π/8 and x = 9·π/8, and the minimum value of the function is; -3 at 5·π/8.

The vertical displacement can be obtained from half the sum of the max and min point as follows;

Vertical displacement = (1 + (-3))/2 = -1

The vertical displacement = -1

The amplitude = Half the distance between the max and min point of the graph

Amplitude, a = (1 - (-3))/2 = 2

The amplitude, a = 2

The period of the graph = 9·π/8 - π/8 = 8·π/8 = π

The period = 2·π/b

Therefore; 2·π/b = π

b = 2·π/π = 2

b = 2

The phase shift = π/8

The cosine function is therefore;

y = 2·cos(2·(x - π/8) - 1

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A very simple explanation:

Solution;

Apperciation: 2.1%

Principal: 150,000

Time: 15 years

Now,

=((0.021×150,000)×15)+150,000

=(3,150×15)+150,000

=47250+150,000

=197,250$

Hence, the house would worth 197,250$ after 15 years

Answer:

6 units

Step-by-step explanation:

The area of a triangle is [tex]A = (b \times h)/2[/tex], where b is base and h is height.

In this case, [tex]b = 6[/tex] and [tex]h = x[/tex]. Plug these into the equation:

[tex]18 = (6x)/2[/tex]

[tex]36 = 6x[/tex]

[tex]x = 6[/tex]

Thus, the answer is 6 units.

Hope this helps!

Answer:

Answer : 264.12cm²

Step-by-step explanation:

Area of a triangle : bh/2

47-18.6 = 28.4

28.4 x 18.6 = 528.24

528.24/2 = 264.12

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Answer:

874.2 cm²

Step-by-step explanation:

The given shape is a parallelogram.

Here,

Base ( b ) = 47 cm

Height ( h ) = 18.6 cm

Formula : -

Area of parallelogram = bh

Area of parallelogram

= bh

= 47 x 18.6

= 874.2 cm²

Hence,

Area of the given parallelogram is 874.2 cm².

There are 36 outcomes in Ec.

What is outcome?
An outcome is a potential outcome of an experiment or trial in probability theory.

The event E represents the sum of two rolled dice being less than or equal to 3. There are only two possible ways to get a sum of 3 or less when rolling two dice: getting a sum of 2 or getting a sum of 3.

If two dice are rolled then sample space is given by,

S = {(1,1), (1,2), (1,3), (1, 4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3, 5), (3,6)

(4,1), (4,2), (4,3), (4, 4) (4,5) (4,6),

(5,1), (5,2), (5,3), (5, 4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,3), (6,6)

n(s) = 36

Event that,

E: sum of two rolled dice is less than 3

[tex]\rm E_c[/tex]= {(1,1)}

n([tex]\rm E_c[/tex]) = 1

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Answer: (-3,-2)

Step-by-step explanation:

 The image of the point (2,−3) under a clockwise rotation of 90° (R_90) about the origin can be found by swapping the x and y-coordinates and changing the sign of the new x-coordinate.

So, the new x-coordinate will be -3 and the new y-coordinate will be -2.

Therefore, the image of the point (2,−3) under a clockwise rotation of 90° (R_90) about the origin is (-3,-2).

Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint called the vertex. The rays or line segments are called the sides of the angle.

Angles are typically measured in degrees or radians, and they are denoted using the symbol ∠. The measure of an angle is the amount of rotation needed to bring one side of the angle into coincidence with the other. A full rotation is 360 degrees or 2π radians.

Angles can be classified into different types based on their measures and their relationships with other angles. Some common types of angles include:

Acute Angle: An angle whose measure is less than 90 degrees.

Right Angle: An angle whose measure is exactly 90 degrees.

Obtuse Angle: An angle whose measure is greater than 90 degrees but less than 180 degrees.

Because BF and CE bisect each other at point D, we know that angles BDC and EDC are congruent, and angles BDF and CDE are also congruent, as they are vertical angles.

By definition of angle bisectors, we know that CD=DE and BD=DF.

Thus, the triangle congruence principle SAS (side-angle-side) allows us to deduce that Triangle BCD is congruent to Triangle ECD, since they share side CD, angle BDC and angle EDC.

Therefore, BC=CE (corresponding sides of congruent triangles are equal) and CE=EF (because CE bisects segment BF).

Thus, BC=EF, and we have proven that BC is equal to EF

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Answer:

last 2 are b

and c

Step-by-step explanation:

Answer:

$ 922.25

Step-by-step explanation:

General equation for simple interest ... B(t)=B(0)[1+rt]B

(0)= inital amount r= simple annual interest rate t= number of yearsFor this problem,

B (2)=$850[0.0425×2}=850×1.085 =$922.25