Three of the interior angle measures of a pentagon are 110°, 115°, and 145°. The remaining angles are congruent. Find the measure of one of the remaining angles.

Answers:

one small box = 30 pounds

one large box = 40 pounds

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Work Shown:

S+L = 70 since the two boxes combine to 70 pounds.

70S = weight of 70 small boxes

50L = weight of 50 large boxes

70S+50L = weight of 70 small and 50 large

70S+50L = 4100

The system of equations is

\(\begin{cases}S+L = 70\\70S+50L = 4100\end{cases}\)

There are a few ways to solve this system. I'll use substitution.

I'm going to isolate L in the first equation like so

S+L = 70

L = 70-S

Which I'll then plug into the other equation to solve for S

70S+50L = 4100

70S+50(70-S) = 4100

70S+3500-50S = 4100

20S+3500 = 4100

20S = 4100-3500

20S = 600

S = 600/20

S = 30

Each small box is 30 pounds.

Use this value of S to find L

L = 70-S

L = 70-30

L = 40

Each large box is 40 pounds.

Like we expect, each large box weighs more compared to any given small box.

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

Check:

Both equations are true for the ordered pair (S,L) = (30,40). Therefore, the answers have been confirmed.

Answer:

y = -4x + 5

Step-by-step explanation:

Linear Formula: y = mx + b

b: The line touches the Y-axis at the fifth unit (0,5)

m: Using the rise-over-run method; the line can be seen going from the coordinates (0,5) to (1,1). Moving from (0,5) to (1,1), you move the plot 4 units downwards and 1 unit to the right; 4/1 = 4. Since the line is sloping downward, the line entire slope value would be -4

With m = -4 and b = 5; your equation is y = -4x + 5

On dividing the positive integer 4,947 by the divisor 6, we get 824 as the quotient and 2 as the remainder. The result of the division of 4947 by 6 we get   \(824\frac{1}{2}\)  or 824.5 as the final answer.

According to the dividend formula,

Dividend = Quotient × Divisor + Remainder. Applying this formula in the given question we get, 4947 as dividend, 6 as divisor, and 2 as the remainder.

On dividing 4,947 by 6, firstly we will be considering only the first two digits i.e. 49. We will be subustracting 6x8 i.e. 48 from 49 and will get 1 as the remainer. 8 will be written on the place of the quotient. Then the next digit 4 will be written in the right of the remainer 1 and the new dividend will be 14. dividing 14 again by 6, we get 2 as remainder and 2 as quotient. this 2 will be written adjecent to the previous quotient. Finally the last digit in 4947 i.e. 7 will be written right to the remainder 2. the dividend finally becomes 27. On dividing it by 6, we get 4 as quotient and the final remainder as 3. The 4 will be written adjecent to the previous two digits at quotient's place. The complete division is shown in the image attachment of this answer.

Finally the quotient becomes 824 on integrating all the quotient digits. The final remainder is 2. The result of 4947/6 is 824.5.

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Answer:

240 trading cards

Step-by-step explanation:

20% of 1200 = .2 × 1200 = 240

(7) The volume of the square base pyramid is 122.5 in³.

(8) The volume of the equilateral base pyramid is 311.8 cm².

(9)  The volume of the square base pyramid is 2,880 ft³.

The volume of the pyramids is calculated by applying the following formula as follows;

(7) The volume of the square base pyramid is calculated as;

V = ¹/₃Bh

where;

V = ¹/₃ x (7 in x 7 in ) x 7.5 in

V = 122.5 in³

(8) The volume of the equilateral base pyramid is calculated as;

V = ¹/₃Bh

V = ¹/₃ x (a²√3/4) x h

V =  ¹/₃ x (12²√3/4) x 15

V = 311.8 cm²

(9)  The volume of the square base pyramid is calculated as;

V = ¹/₃Bh

where;

V = ¹/₃ x (24 ft x 24 ft ) x 15 ft

V = 2,880 ft³

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The probability of getting the specific sequence t, h, h, h, h, t, t, t, t, t, t when tossing a coin 11 times is 1/2048.

To find the probability of this specific sequence occurring, we need to use the formula for the probability of a specific sequence of independent events:

P(A and B and C and D and E and F and G and H and I and J and K) = P(A) * P(B) * P(C) * P(D) * P(E) * P(F) * P(G) * P(H) * P(I) * P(J) * P(K)

In this case, A represents the first toss being a tails (t), B represents the second toss being a heads (h), and so on until K represents the eleventh toss being a tails (t).

Using the given sequence, we can calculate the individual probabilities for each toss:

P(A) = 1/2 (since there is a 50/50 chance of getting either heads or tails on the first toss)

P(B) = 1/2 (since there is a 50/50 chance of getting heads on the second toss after getting tails on the first toss)

P(C) = 1/2 (since there is a 50/50 chance of getting heads on the third toss after getting heads on the second toss)

P(D) = 1/2 (since there is a 50/50 chance of getting heads on the fourth toss after getting heads on the third toss)

P(E) = 1/2 (since there is a 50/50 chance of getting heads on the fifth toss after getting heads on the fourth toss)

P(F) = 1/2 (since there is a 50/50 chance of getting tails on the sixth toss after getting heads on the fifth toss)

P(G) = 1/2 (since there is a 50/50 chance of getting tails on the seventh toss after getting tails on the sixth toss)

P(H) = 1/2 (since there is a 50/50 chance of getting tails on the eighth toss after getting tails on the seventh toss)

P(I) = 1/2 (since there is a 50/50 chance of getting tails on the ninth toss after getting tails on the eighth toss)

P(J) = 1/2 (since there is a 50/50 chance of getting tails on the tenth toss after getting tails on the ninth toss)

P(K) = 1/2 (since there is a 50/50 chance of getting tails on the eleventh toss after getting tails on the tenth toss)

Multiplying these probabilities together gives us the probability of getting the sequence t, h, h, h, h, t, t, t, t, t, t:

P(t, h, h, h, h, t, t, t, t, t, t) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/2048

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Answer:

We can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To do this, we can rearrange the terms as follows:y = 9 - xy = -1x + 9

This gives us a slope of -1 and a y-intercept of 9. We can plot the y-intercept at (0, 9) and use the slope to find another point on the line. The slope tells us that for every increase of 1 in x, the value of y decreases by 1. So, starting from (0, 9), we can move one unit to the right and one unit down to get another point (1, 8). We can continue this process to find more points or connect the two points we already have to draw a line.

Let me know if this helped by hitting brainliest! If you have any questions, please comment below!

The resulting graph should be a straight line that starts at the point (0, 9) on the y-axis and intersects the x-axis at the point (9, 0). The line slants downward from left to right.

Here, we have,

We can rewrite the equation in slope-intercept form,

y = mx + b,

where m is the slope and b is the y-intercept.

To do this, we can rearrange the terms as follows:

y = 9 - x

y = -1x + 9

This gives us a slope of -1 and a y-intercept of 9.

We can plot the y-intercept at (0, 9) and use the slope to find another point on the line.

The slope tells us that for every increase of 1 in x, the value of y decreases by 1.

So, starting from (0, 9), we can move one unit to the right and one unit down to get another point (1, 8).

We can continue this process to find more points or connect the two points we already have to draw a line.

To graph the equation y = 9 - x, you can follow these steps:

Step 1: Create a table of values. Choose some x-values and substitute them into the equation to find the corresponding y-values. For simplicity, let's choose three values for x:

x | y = 9 - x

0 | 9 - 0 = 9

3 | 9 - 3 = 6

6 | 9 - 6 = 3

Step 2: Plot the points. Use the x-values from the table and their corresponding y-values to plot the points on the graph. The points are (0, 9), (3, 6), and (6, 3).

Step 3: Draw the line. Connect the plotted points with a straight line. The line should pass through all the plotted points.

The resulting graph should be a straight line that starts at the point (0, 9) on the y-axis and intersects the x-axis at the point (9, 0). The line slants downward from left to right.

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Answer:

Answer C:     102

Step-by-step explanation:

The correct answer for the question is 102. I did the quiz and got it right.

                    Hope this helps you!

                                        ~Me ^^

To solve this problem, we need to find the proportion of bulbs that have a life less than 700 hours. We can do this by finding the probability that a randomly selected bulb has a life less than 700 hours and then converting that probability to a percentage.

Since the distribution is symmetric about the mean, we can assume that it is approximately normal. We can then use the normal distribution to find the probability that a randomly selected bulb has a life less than 700 hours.

To do this, we need to standardize the value 700 hours by subtracting the mean and dividing by the standard deviation:

z = (700 - 900) / 50 = -2

This means that 700 hours is 2 standard deviations below the mean. We can use a standard normal table (or a calculator) to find the probability that a randomly selected bulb has a life less than 700 hours:

P(x < 700) = P(z < -2) = 0.0228

This probability is very small, so we can convert it to a percentage by multiplying by 100:

0.0228 * 100 = 2.28%

Therefore, at most 2.28% of the bulbs are expected to fail to last even 700 hours.

A percentage is a figure or ratio that in mathematics represents a portion of one hundred. It is one of the ways to indicate a dimensionless relationship between two numbers; other ways include ratios, fractions, and decimals. The symbol "%" is frequently written after the number to represent percentages.

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Answer:

Step-by-step explanation:

SOLVING

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

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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A drop of water is denser than a ping-pong ball.

Usually, water is made of particles that are firmly pressed together. In differentiation, plastic (the material ping pong balls are made of) may be a lightweight fabric and the particles are not as firmly stuffed together.

The thickness of a ping pong ball is 0.0840 g/cm³, though water’s thickness is 997 kg/m³. Subsequently, ping pong balls aren’t about as thick as water and will continuously coast and surface greatly quickly.

The ping pong ball appears to oppose gravity and coast within the air.

Ping-pong balls drift within the water since they are amazingly lightweight, empty, and filled with air. Too, the water’s surface pressure makes it simple for the ping pong ball to drift.

In expansion, water is denser than ping pong balls, making them look for the most noteworthy point of water.

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The sound which we hear when the pig pong ball is bounced on the floor

is 19.48 DB

The repeating of sounds, especially in rhyme, is the form of repetition that most people connect with poetry. Alliteration, assonance, and onomatopoeia are other sound patterns in poetry that give additional meaning in addition to rhyme. Every one of these audio elements has a certain purpose in a poem.

a) \(\sum \ log(n)\)

by expanding the series for each value of n is

log (1) + log (2) + log(3) + log (4) + ......... + log ( 96)

simplify the expanded form we get

0 + 0.3010 + 0.4771+0.6020 ......................... + 1.982

=> 149.9963

b) \(\sum_{n=0}\) to infinity \(\sqrt{0.9^n}\)

formula for the sum of number in geometric progression

is  a/1-r

to find the ratio of the successive terms

plugging into the formula

r = \(\frac{a_{n+1}}{a_n}\)

r = \(\frac{\sqrt{0.9^{n+1}} }{\sqrt{0.9^n} }\)

=> r = \(\frac{\sqrt{0.9^n \times 0.9} }{\sqrt{0.9^n} .1}\)

=> r = \(\frac{\sqrt{0.9} }{1}\)

=> r = \(\sqrt{0.9}\)

=> a = \(\sqrt{0.9^0}\)

=> a = \(\sqrt{1}\)

=>  a= 1

by applying the formula having the value a =1 is

\(\frac{1}{1-\sqrt{0.9} }\)

rationalize the denominator by multiplying with \(1+\sqrt{0.9}\)

=> \(\frac{1+\sqrt{0.9} }{(1-\sqrt{0.9} ) (1+\sqrt{0.9}) }\)

=> 19.4868

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Answer:

no

Step-by-step explanation:

because,THE MOON IS SMALLER ACROSS (IN DIAMETER) THAN THE UNITED STATES IS WIDE. If the Earth were hollow, about 50 moons would fit inside. a. THE MOON IS SMALLER THAN THE EARTH: FIFTY MOONS WOULD FILL THE EARTH.

Answer:

44 cm³

Step-by-step explanation:

If you break up this shape into 2 pieces you get a rectangle with the measurements of 2, 2, and 5 and another rectangle with the measurements of 2, 2, and 6. You then multiply 2, 2, and 5 together which will get you 20, and multiply 2, 2, and 6 together which will get you 24. You will then add both products which will get you 44. Since the measurement is in centimeters and it is a 3 dimensional shape it will then become 44 cm³.

Answer:

10=Z and 10=Y

Step-by-step explanation:

since it is a 45, 45, 90 triangle

both Z and Y will be the same length

the hypotenuse has a length of \(x\sqrt{2}\) with x being the length of the legs

Since the length of this triangle's hypotenuse is \(10\sqrt{2}\) the side length would be 10

Hope that helps :)

By solving the generated equation, Calvin caught 16 smallmouth bass and 9 largemouth bass.

What is meant by equation?

An equation states that the two expressions have the same value or are equivalent to each other. Equations are used in various areas of mathematics, science, engineering, and everyday life to describe relationships and solve problems.

Let x represent the number of smallmouth bass that Calvin caught, and y represent the number of largemouth bass that he caught.

From the problem, we know that the total number of fish that Calvin caught is 25:

x + y = 25

We also know that the number of smallmouth bass that Calvin caught is 2 less than double the number of largemouth bass that he caught:

x = 2y - 2

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:

y = 25 - x

Substituting this into the second equation, we get:

x = 2(25 - x) - 2

Simplifying this equation, we get:

x = 48 - 2x

Solving for x, we get:

3x = 48

x = 16

Substituting this value of x back into either of the original equations, we can solve for y:

y = 25 - x = 25 - 16 = 9

Therefore, Calvin caught 16 smallmouth bass and 9 largemouth bass.

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Answer:

x>=-11/4

Step-by-step explanation:

f(x)=\(\sqrt{4x+9+2}\)

The number which has a square root has to be greater than or equal to 0.

Hence, 4x+9+2>=0

Solve the inequality:

4x+9+2>=0

4x+11>=0

4x>=-11  ==> subtract 11 on both sides to isolate x

x>=-11/4 ==> divide both sides by 4

(a) The PDFs of U and V are given by: fU(u)=1/π for −1≤u≤1 and fV(v)=1/π for −1≤v≤1. The expectations of U and V can be found by using integration. E(U)=∫−1 1u/πdu=0, and E(V)=∫−1 1v/πdv=0. The covariance between U and V is given by Cov(U,V)=E[(U-E(U))(V-E(V))]=E(UV)-E(U)E(V)=E(UV)=∫−1 1uv/πdudv=0. Since Cov(U,V)=0, U and V are independent.
(b) The density of W is given by fW(w)=∫−1 1∫−1 1uv/πdudv=2/π√w for 0≤w≤1.
(c) Let R=θU and T=θV. The joint distribution of (R, T) can be found by using integration. The PDF of (R, T) is given by f(r,t)=1/πθ2 for −θ≤r,t≤θ.

In summary, the PDFs of U and V are given by fU(u)=1/π for −1≤u≤1 and fV(v)=1/π for −1≤v≤1. The expectations of U and V are E(U)=0 and E(V)=0, and the covariance between U and V is Cov(U,V)=0, which means U and V are independent. The density of W is given by fW(w)=2/π√w for 0≤w≤1. The joint distribution of (R, T) is given by f(r,t)=1/πθ2 for −θ≤r,t≤θ.

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The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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(a) The critical value of t with 10 degrees of freedom and a 0.05 level of significance is approximately 1.812.

(b) The critical value of t with 29 degrees of freedom and a 0.025 level of significance is approximately 2.045.

(c) The critical value of t with 17 degrees of freedom and a 0.1 level of significance is approximately 1.740.

(a) For a 90% confidence interval based on n-12 observations, we would need to use the t-distribution with n-1 degrees of freedom. Since n-12 observations are given, the degrees of freedom would be n-1-12 = n-13. Using a t-table or calculator, we can find the critical value of t with n-13 degrees of freedom and a 0.05 level of significance (since we are calculating a two-sided confidence interval)

(b) For a 95% confidence interval from an SRS of 30 observations, we would again need to use the t-distribution with n-1 degrees of freedom. Since n=30 observations are given, the degrees of freedom would be 30-1 = 29. Using a t-table or calculator, we can find the critical value of t with 29 degrees of freedom and a 0.025 level of significance (since we are calculating a two-sided confidence interval).

(c) For an 80% confidence interval from a sample of size 18, we would again need to use the t-distribution with n-1 degrees of freedom. Since n=18 observations are given, the degrees of freedom would be 18-1 = 17. Using a t-table or calculator, we can find the critical value of t with 17 degrees of freedom and a 0.1 level of significance (since we are calculating a two-sided confidence interval).

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Solving a linear equation we can see that for 7.5 miles, both services charge the same amount.

For food drivers, there is a fixed cost of $4 plus $0.25 per mile, so if you drive x miles the cost is:

f(x) = $4 + $0.25*x

For totally takeout, the fixed cost is $3.25 and they chare $0.35 per mile, so the cost equation is:

g(x) = $3.25 + $0.35*x

Both services charge the same if:

g(x) = f(x)

So we need to solve the linear equation:

$4 + $0.25*x =  $3.25 + $0.35*x

$4 - $3.25 = $0.35*x  - $0.25*x

$0.75 = $0.10*x

$0.75/$0.10 = x = 7.5

So, for 7.5 miles, both services charge the same amount.

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Using the order of operations, the expression can be simplified as  

9 + 1.34 + 62.88 = 73.22

The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.

Remember PEMDAS when simplifying multi-step expressions, i.e.:

P (Parentheses)

E (Exponents, Powers and Square Roots)

MD (Multiplication and Division, left-to-right)

AS (Addition and Subtraction, left-to-right)

The expression given in the problem is:  9 + 1.34 + 1 2 (3.50 +1.74)

Apply the above operation order:

Step 1: solve the addition inside the parenthesis

9 + 1.34 + 1 2 (3.50 +1.74)  =  9 + 1.34 + 1 2 (5.24)

Step 2: Multiply the result by 12

9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88

Step 3: Apply addition from left to right

9 + 1.34 + 62.88 = 73.22

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Answer:

We have a 30°-60°-90° right triangle, so the length of the longer leg is √3 times the length of the shorter leg.

x = 4√3

Answer: 9 hours

Step-by-step explanation:

Answer:

what numbers are located between (-10 and (-5 on a number line

Answer:

$14

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

It's A because all of them have exactly one output

it is a right triangle lengths 6 8 and 10.

In this issue:

Then:

\(& 6^2+8^2=10^2 \\\)

\(& 36+64=100 \\\)

\(& 100=100\)

Identity, so it is a right triangle.

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Answer:

candy:6

gum:4

The answer is that because I did systems from a word problem

Answer:

C. G(x) is a negative number with a small absolute value

Step-by-step explanation:

As x increases, G(x) goes towards 0 from the a negative quadrant.

Answer:

you need 13

Step-by-step explanation:

because you need at least 5 and a 8 water bottles and 8+5 is 13