Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
16 yd
6 yd
14 yd
8 yd
7 yd

A) R = -19t + 1890 B) 11 years from now, the total oil reserves will be 1681 billions of barrels. C)  The world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now.

The slope of a line represents the rate of change between the x and y variables, or the rise over the run. A positive slope means that the line is increasing from left to right, while a negative slope means that the line is decreasing from left to right. A slope of zero means that the line is horizontal, while an undefined slope means that the line is vertical.

A) The rate of decrease in oil reserves is 19 billion barrels per year, which can be represented as a slope of -19. The initial oil reserves are 1890 billion barrels, which is the y-intercept. Therefore, the linear equation for the total remaining oil reserves R, in terms of t (the number of years since now) is:

R = -19t + 1890

B) To find the total oil reserves 11 years from now, we can substitute t = 11 into the equation:

R = -19(11) + 1890

R = -209 + 1890

R = 1681 billion barrels

Therefore, 11 years from now, the total oil reserves will be 1681 billions of barrels.

C) If no other oil is deposited into the reserves, the reserves will be completely depleted when R = 0. We can use the linear equation to find how long it will take for the reserves to reach 0:

0 = -19t + 1890

19t = 1890

t = 99.47 years

Therefore, the world's oil reserves will be completely depleted (all used up) approximately 99.47 years from now, assuming no new reserves are discovered or added.

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Answer: 8.2 weeks.

Step-by-step explanation: If y = 4*3^t, then 600 = 4*3^t. Therefore, t = log3 (600/4), which is approximately 8.2 weeks.

Answer:

Two monomials with the quotient 24a2b5 are:

12a b³

48a³ b²

Step-by-step explanation:

In square prism , A cracker box in the shape of a square prism with a base side length of   [tex]SA - \frac{2S^{2} }{4S} = h[/tex].

What is square prism?

The bases of a square prism are square, and the other four faces are rectangles. A square prism is a cuboid object in three dimensions.

                                    Angles and sides that are in opposition to one another are congruent. A magnet bar is an illustration of the shape of a square prism.

we know that'

The formula to calculate the surface area of a square prism is

          [tex]Q = 2s^{2} + 4sh[/tex]

  subtract 2s² both sides

    SA - 2s² = 4sh

  Divide by 4s both sides

     [tex]SA - \frac{2S^{2} }{4S} = h[/tex]

   Rewrite

   [tex]SA - \frac{2S^{2} }{4S} = h[/tex]

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Answer:

Inverse Operation

Step-by-step explanation:

In answering the question above, the solution is If a/b = 1/4 and c/d = 1/3, fraction then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are stated in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You may assess it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a whole number or object.

Let's start by decomposing { into two fractions:

[tex]{ = a/b + c/d\\\\{ = (ad + bc)/bd[/tex]

If [tex]a/b = 1/2 and c/d = 1/3, then ad + bc = (1/2)(bd/2) + (1/3)(bd/3) = bd/3 + bd/6 = 3bd/6 + bd/6 = 4bd/6 = 2/3,[/tex] which works.

If [tex]a/b = 1/2 and c/d = 1/4, then ad + bc = (1/2)(bd/2) + (1/4)(bd/4) = bd/4 + bd/8 = 2bd/8 + bd/8 = 3bd/8,[/tex] which doesn't work.

If [tex]a/b = 1/2 and c/d = 1/5, then ad + bc = (1/2)(bd/2) + (1/5)(bd/5) = bd/4 + bd/25 = 25bd/100 + 4bd/100 = 29bd/100[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/4, then ad + bc = (1/3)(bd/3) + (1/4)(bd/4) = bd/9 + bd/16[/tex], which doesn't work.

If[tex]a/b = 1/3 and c/d = 1/5, then ad + bc = (1/3)(bd/3) + (1/5)(bd/5) = bd/9 + bd/25,[/tex] which doesn't work.

If a/b = 1/4 and c/d = 1/3, then ad + bc = (1/4)(bd/4) + (1/3)(bd/3) = bd/16 + bd/9, which doesn't work.

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Answer:

Step-by-step explanation:

Mark decompose 5/6 into three fractions using fractions : 1/3, 5/18, 2/9

What is fraction?

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given, fraction

5/6

Multiplying 3 with both numerator and denominator

15/18

= (6 + 5 + 4)/18

= 6/18 + 5/18 + 4/18

= 1/3 + 5/18 + 2/9

Hence, 1/3, 5/18, 2/9 are fractions Mark used to decompose 5/6.

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Answer: 9g+10

Step-by-step explanation:

Simple addition 6+3=9

Since 10 doesnt have a variable you just add it to the end of the equation, make sure to keep the sign = 9g-10

The correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression, [tex]\sqrt[3]{24} \sqrt[4]{32}[/tex], we need to simplify it,

Factoring them,

24 = 2 x 2 x 2 x 3

32 = 2 x 2 x 2 x 2 x 2

Therefore,

[tex]\sqrt[3]{24} = 2\sqrt[3]{3}[/tex]

[tex]\sqrt[4]{32} = 2\sqrt[4]{2}[/tex]

[tex]\sqrt[3]{24} \sqrt[4]{32}[/tex] =  [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

Hence, the correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]

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The probability that a random sample of 50 seniors has a mean score of at most 415 is given as follows:

0.1894 = 18.94%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 425, \sigma = 80, n = 50, s = \frac{80}{\sqrt{50}} = 11.31[/tex]

The probability that they scored at most 415 is the p-value of Z when X = 415, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (415 - 425)/11.31

Z = -0.88

Z = -0.88 has a p-value of 0.1894.

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Answer:

Ayanda will receive R20,160, Zipho will receive R15,120, and Palesa will receive R10,080.

Step-by-step explanation:

We can use the ratio of 4:3:2 to find the total number of parts:

4 + 3 + 2 = 9

This means that the money will be divided into 9 equal parts, and Ayanda will get 4 parts, Zipho will get 3 parts, and Palesa will get 2 parts.

To find the value of one part, we divide the total amount by 9:

45,360 / 9 = 5,040

Therefore, one part is worth R5,040.

Now we can find the amount of money each person will receive by multiplying their respective parts by the value of one part:

Ayanda: 4 parts × R5,040/part = R20,160

Zipho: 3 parts × R5,040/part = R15,120

Palesa: 2 parts × R5,040/part = R10,080

Therefore, Ayanda will receive R20,160, Zipho will receive R15,120, and Palesa will receive R10,080.

Answer:

Below

Step-by-step explanation:

1  8/10  = 18/10

18 / 10   pound  *  $ 4.10 / pound  =  (18 * 4.1) / 10 =  73.8 /10 = $ 7.38

( see how the unit 'pound' cancels out and you are left with  $  ???)

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{22\% of 72}}{\left( \cfrac{22}{100} \right)72}\implies 15.84~\hfill \underset{ new~price }{\stackrel{ 72~~ + ~~15.84 }{\text{\LARGE 97.84}}}[/tex]

The equation -cd is always defined, regardless of the values of the variables c and d.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

The equation cd

Now,

The equation -cd is always defined, regardless of the values of the variables c and d.

The expression -cd represents the product of two numbers, -c and d. Multiplication is a well-defined operation for all real numbers, including zero. so, neither c nor d need to be non-zero for the expression to be defined.

Therefore, the equation -cd is defined for all values of a, b, c, and d, including zero

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Equation of best fit line on scatter plot is y = 30x + 40

Correct option is D.

A straight line is an infinite one-dimensional shape with no width. An infinite combination of points connected on either side of the point. A straight line has no curves. It can be horizontal, vertical, or slanted. An angle drawn between any two points on a straight line is always 180 degrees.

Given,

Scatter plot of the data of studying time of students

By the graph, point on the line are (0, 40) and (2,70)

Equation of the line

y - y₁ = ((y₂-y₁)/(x₂-x₁))(x-x₁)

y - 40 = ((70-40)/(2-1))(x-0)

y - 40 = (30/1)x

y - 40 = 30x

y = 30x + 40

Hence, y = 30x + 40 is the equation of the best fit line in scatter plot.

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Answer:

Yes, it will fit.

Step-by-step explanation:

To determine whether 375 cubic inches of sand will fit into the given rectangular prism, we need to calculate the volume of the prism and compare it to the amount of sand.

The formula for the volume of a rectangular prism is:

Volume = Base x Height x Width

In this case, the base of the prism is 5 by 7 inches, so the area of the base is:

Area of Base = 5 inches x 7 inches = 35 square inches

The height of the prism is 9 inches. Therefore, the volume of the prism is:

Volume = Base x Height = 35 square inches x 9 inches = 315 cubic inches

So, the volume of the prism is 315 cubic inches, which is less than the amount of sand Jack has (375 cubic inches). Therefore, all of the sand will fit inside the rectangular prism with room to spare.

In summary, the sand will fit inside the rectangular prism because the volume of the prism is greater than the amount of sand Jack has.

Answer:

Sides:

MX = 4cm

BX = 8cm

BM = 6.928...cm

Angles:

m = 90°

b = 30°

x = 60°

Step-by-step explanation:

We've been given 3 pieces of info that we can use, which is more than enough

Using the sine rule, we can find the hypotenuse:

[tex]\frac{4cm}{sin30} = \frac{BXcm}{sin90}[/tex]→[tex]\frac{4sin90}{sin30} =BX = 8cm[/tex]

Now we can use Pythagoras' theorem to find the last side:

[tex]a^2+b^2=c^2[/tex] →  [tex]b^2\ = c^2-a^2[/tex] → [tex]64 - 16 = b^2 = 48[/tex] → [tex]\sqrt{48} =6.928...cm[/tex]

And since we know two of the angles, we can find the third:

[tex]x = 180 - (30 + 90) = 180 - 120 = 60[/tex]°

Answer:

Below

Step-by-step explanation:

REMEMBER: for a right triangle  sin (30) = opposite LEG/ hypotenuse

 so sin 30 =  4 / hypotenuse         now, with a calculator sin 30 = 1/2

           1/2   = 4 / hypotenuse      so hypotenuse = 8

Now it is a right triangle so Pythagorean theorem applies

 hyp ^2 = 4 ^2   +   BM^2

  8^2 = 4^2 + BM^2

     48 = BM^2     so  BM = sqrt (48 ) = 4 sqrt 3

Finally, all of the internal angles of ANY triangle sum to 180 °

  so angle x = 180 - 90 - 30 = 60°

The length of the diagonals will be WZ = XZ = 11 units.

A diagonal in geometry is a line segment that connects two polygonal or polyhedral vertices when they are not on the same edge. Any sloping line is known as a diagonal informally.

The length of the two diagonals of the rectangle is equal. The value of x will be calculated as,

6x - 7 = 3x + 2

3x = 9

x = 3

WZ = 6x - 7

WZ = 6 x 3 - 7

WZ = 18 - 7

WZ = 11

XZ = 3x + 2

XZ = 3 x 3 + 2

XZ = 11

Therefore, the length of the diagonals will be WZ = XZ = 11 units.

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The constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.

What is the exponential functions?

An exponential function is a mathematical function of the form:

[tex]f(x) = a^x[/tex]

The given formula for the number of visitors to the county parks system is:

[tex]A = 20.6(1.03)^t[/tex]

where t is the number of years after 2010 and A is the number of visitors in thousands.

To find the constant percent rate of change per unit interval, we can take the derivative of A with respect to t:

[tex]dA/dt = 20.6(1.03)^t * ln(1.03)[/tex]

The constant percent rate of change per unit interval is given by the expression:

r = (dA/dt) / A

Substituting the values of dA/dt and A, we get:

[tex]r = [20.6(1.03)^t * ln(1.03)] / [20.6(1.03)^t]\\r = ln(1.03)\\r = 0.0305[/tex]

Hence, the constant percent rate of change per unit interval is approximately 0.0305 or 3.05%.

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Answer:

Step-by-step explanation:

y = √24²+32² = √1600 = 40

find base angle Ф on the right:

Ф = sin⁻¹(32/40) = 53.13

find other base angle (sum of interior angles of a Δ is 180):

180 - 90 - 53.13 = 36.87

now you can use the Law of Sines to find z, x:

40/sin36.87 = z/sin53.13 = (x+24)/sin90

z = 40(sin53.13)/sin36.87 = 53.33

sin36.87(x+24) = 40(sin90)

x+24 = 40/sin36.87 = 66.66

x = 66.67 - 24 = 42.67

double check the answers:

y² + z² = (x+24)²

40² + 53.33² = (42.67 + 24)²

1600 + 2892 = 4444

4444 = 4444  answers are correct!

A = 4 ft × 3ft = 12 ft²

∴ The area of the base of the prism is 12 ft².

The y-value of the solution of the system of equations is given as follows:

y = -1.

The system of equations for this problem is defined as follows:

Adding the two equations, the value of y can be obtained as follows, as the x-variable is eliminated:

6y = -6

y = -6/6

y = -1.

Hence option F is correct.

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Answer:

55 KG

Step-by-step explanation:

To convert pounds to kilograms, we can use the conversion factor 1 kg = 2.2 lbs.So,121 lbs = (121 lbs) * (1 kg/2.2 lbs)Simplifying the expression, we have121 lbs ≈ 55.0 kgRounding to the nearest tenth, we get the final answer:121 lbs ≈ 55.0 kg

Answer:

To convert 121 pounds into kilograms, we can use the conversion factor:

1 kg = 2.2 lb

Dividing both sides of this equation by 2.2, we get:

1 lb = 0.454545 kg (rounded to the nearest tenth, this is 0.5 kg)

Therefore, we can convert 121 pounds to kilograms by multiplying by 0.454545:

121 lb * 0.454545 kg/lb = 54.884545 kg

Rounding this to the nearest tenth gives:

54.9 kg

Therefore, 121 pounds is approximately equal to 54.9 kilograms when rounded to the nearest tenth.

Answer:

30 miles

Step-by-step explanation:

(12 miles/inch)(2.5 inches) = 30 miles

Barbara's weekly average for the four-week period is 65 minutes.

What is the average?

The average, also known as the arithmetic mean, is a measure of central tendency that represents the typical value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of numbers.

To find Barbara's weekly average for the four-week period, we need to add up her weekly totals and divide the sum by 4 (since there are four weeks in the period):

Average = (48 + 115 + 62 + 35) / 4

= 260 / 4

= 65

Therefore, Barbara's weekly average for the four-week period is 65 minutes.

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Answer:4

Step-by-step explanation:12/3

Correct option is D. randomly sampling 50 batteries throughout the day and testing to see if they work would provide the most valid results.

A sample is described as a smaller, more manageable representation of a larger group. a smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.

The sample may be biased if it is taken from the first 25 batteries made each day (option A) or the last 25 batteries made each day (option B).

The first and final batteries made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent throughout the day.

Although battery quality can change during the day, sampling the first 50 batteries produced each day (option C) may also add bias into the sample.

The ideal course of action is to randomly select 50 batteries throughout the day (option D), since this helps to ensure that the sample is reflective of the general caliber of batteries manufactured that day.

Random sampling reduces the possibility of bias into the sample.

A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.

Therefore, option D would provide the most valid results.

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The translation that occurred to the segment is: B. The segment was shifted to the right four units and up five units.

Translation is a transformation in which an object is moved without being rotated, resized or distorted. It involves sliding the object a certain distance in a certain direction, while maintaining its shape and size. The resulting image of the object is congruent to the original object, meaning that they have the same size and shape.

To find the translation that occurred to the segment, we need to calculate the distance between point A and its image A' and the direction in which the translation occurred.

The distance between A and A' is given by:

√((7-3)² + (2-(-3))²) = √(16 + 25) = √(41)

So the segment was translated by a distance of √(41).

To find the direction of the translation, we can subtract the coordinates of A from the coordinates of A':

(A'x - Ax, A'y - Ay) = (7-3, 2-(-3)) = (4, 5)

So the segment was shifted to the right four units and up five units.

Therefore, the correct answer is B. The segment was shifted to the right four units and up five units.

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The highest value and lowest value of x is domain, here domain is [1, -3]

The highest value and lowest value of y is range, here range is [8, -3].

Mathematical operations are comparable to those of a soda vending machine. You can choose from a variety of sodas when you deposit a certain sum of money. Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.

A soda can be purchased with quarters and one dollar bills. If pennies are put into the machine, no soda flavour will be provided. As a result, the domain represents the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a soda machine won't give you a cheeseburger. The range represents the potential outputs we can have in this situation, that is, the  flavors of soda in the machine.

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As a resuIt, 10 (181)/181 is the sin vaIue that cοmes cIοsest tο 10 √(181)/√181. B is the apprοpriate answer, sο.

The cοst οr price οf sοmething, aIsο knοwn as its mοnetary vaIue.

The right-angIed triangIe fοrmed by the angIe's terminaI side and the pοints (-9, 10) can be caIcuIated using the Pythagοrean Theοrem tο determine the Iength οf a hypοtenuse:

h = √((-9)² + 10²) = √(81 + 100) = √(181)

Sin is pοsitive because the pοsitiοn (-9, 10) οccupies the secοnd quadrant. We are abIe tο determine the actuaI amοunt οf sin that use the definitiοn οf sin:

sin(theta) = οppοsite/hypοtenuse = 10/√(181)

We can cοmbine the twο parts οf this fοrmuIa by √181 tο οbtain the fοIIοwing resuIt:

sin(theta) = 10 × √(181)/√(181)√(181) = 10√(181)/181

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Answer:

Where's the question...