In ΔSTU, TU = 11, US = 17, and ST = 18. Which statement about the angles of ΔSTU must be true?

The correct answer is: Jeff will use 8 oz of powder and 24 cups of water to make 8 boxes of gelatin.

To determine the amount of powder and water Jeff will use to make 8 boxes of gelatin, we need to find the pattern in the given table. By examining the table, we can see that for every 3 boxes of gelatin powder (oz), 9 cups of water are used. This implies that the ratio of powder to water is 3:9, which can be simplified to 1:3.

Since Jeff wants to make 8 boxes of gelatin, we can multiply the ratio by 8 to find the corresponding amounts of powder and water.

For the powder, we have:

1 part (powder) * 8 (number of boxes) = 8 parts of powder.

Therefore, Jeff will use 8 oz of powder.

For the water, we have:

3 parts (water) * 8 (number of boxes) = 24 parts of water.

Therefore, Jeff will use 24 cups of water.

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The monthly expenditure of September for question 9 and 10 are respectively $107.91 and $19892.25

From the question, it is rather easy to figure out. We are given expenditures from May through August, September missing but we are also provided with the average expenditure.

We know that the average expenditure is given as

sum of expenditure of all the months / number of months

So, for number 9, we have

[(112.11 + 97.13 + 106.45 + 121.85 + x) / 5] = 109.09

(437.54 + x) / 5 = 109.09....... if we cross multiply

437.54 + x = 109.09 * 5

437.54 + x = 545.45

x = 545.45 - 437.54

x = 107.91

And for number 10, we have

[(23687.12 + 19871.03 + 20056.90 + 24510.30 + y) / 5] = 21603.52

(88125.35 + y) / 5 = 21603.52......... if we cross multiply

88125.35 + y = 21603.52 * 5

88125.35 + y = 108017.6

y = 108017.6 - 88125.35

y = 19892.25

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The approximate area of the green visible portion of the bottom section is around 33.51 square inches.

Let x be the width of the green visible portion of the bottom section in inches. Then, the width of the yellow top of the bottom section is x + 2, and the width of the yellow top of the upper section is (x + 2) + 2 = x + 4.

Since the area of a circle is given by A = πr^2, and the yellow top of the upper section has an area of 12.56 square inches, we can set up the equation:

12.56 = π((x+4)/2)^2

Simplifying and solving for x, we get:

x ≈ 4.02

Therefore, the width of the green visible portion of the bottom section is approximately 4.02 inches, and its area is:

A ≈ (π/4)(x+2)^2 - 12.56 ≈ 33.51 square inches.

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Answer:

-5/4

Step-by-step explanation:

Pick two points on the line

(-4,0) and (0,-5)

We can use the slope formula

m = (y2-y1)/(x2-x1)

   = ( -5 -0)/(0 - -4)

    = (-5-0)/(0+4)

    = -5/4

Answer: -5/4

Step-by-step explanation:

Pick two points on the line

(-4,0) and (0,-5)

We can use the slope formula

m = (y2-y1)/(x2-x1)

  = ( -5 -0)/(0 - -4)

   = (-5-0)/(0+4)

   = -5/4

- Chilio

it is a because it is the line is in the spot we're it is ststop to go

The sampling distribution of difference between means approximates a normal curve whose mean is zero.

The sampling distribution means the probability distribution based on the large number of samples of size n from the given population

Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.

Here they used the normal curve, sot its mean value is zero

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The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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You can find the decimal forms of 3/12 and 2/9 by dividing the numerators of each of the fraction by its denominator.

The decimal form of 3/12 is 0.25.

The decimal form of 2/9 is 0.222.

The decimal form of 3/12 is a terminating decimal.

The decimal form of 2/9 is a repeating decimal.

The greater fraction is 3/12. This is because the hundredth value of 3/12 in decimal form is greater than that of 2/9.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above and the denominator is the number below.

A decimal is a number that is made up of integers and non-integers that are separated by a decimal point. The integers are before the decimal point. The non-integers are after the decimal point. In order to convert a fraction to a decimal, divide the numerator by the denominator.

3 / 12 = 0.25

2 / 9 = 0.22

A terminating decimal is a decimal that ends. A repeating decimal is a number that does not end. An example of a terminating decimal is 0.25, 0.1. An example of a repeating decimal is 0.33, 0.222.

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The two vectors parallel to the plane are AB(8, -5, 4) and AC(0, 7, 6).

The vector perpendicular to the plane is (-58, -48, 56).

Vector AB is parallel to the plane since it connects two points on the plane, A and B.

The coordinate point is calculated as;

AB = B - A

= (11, -5, 2) - (3, 0, -2)

= (8, -5, 4)

Vector AC is also parallel to the plane since it connects two points on the plane, A and C.

The coordinate point is calculated as;

AC = C - A

= (3, 7, 4) - (3, 0, -2)

= (0, 7, 6)

To find a vector perpendicular to the plane, we will take the cross product of two vectors in the plane, such as AB and AC.

AB x AC = (8, -5, 4) x (0, 7, 6)

=  (-58, -48, 56)

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Answer:

Step-by-step explanation:

455: 5 * 91

455: 5 * 7 * 13

the 5 is easy to find. If some number ends in 5 it is divisible by 5.

91 is not so easy.

91 is not divisible by 2. 91 is an odd number.

It is not divisible by 3. 9 + 1 = 10 which is not divisible by 3

We have already covered 5.  so we start a new series of numbers

91 / 7 = 13 and we are done.

Answer:

5,7,13

Step-by-step explanation:

455

  ↓

91 x 5

  ↓

13 x 7

Answer:

The point of intersection between 2x+3y=12 and 2x-y=4 is (3,2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Massachusetts Body of Liberties were technically the first ever legal code system established by the colonists, and established a central court that had full rights and jurisdictions over the citizens.

I disagree with the student's claim. The number of decimal places in the product may not always be the same as the total number of decimal places in the factors.

In multiplication, the total number of decimal places in the product is determined by adding the decimal places in the factors. For example, if we multiply 2.5 by 0.3, both factors have one decimal place. When we multiply them, the product is 0.75, which also has one decimal place. In this case, the student's claim holds true.

However, in other operations like division or addition/subtraction, the number of decimal places in the product can differ from the total number of decimal places in the factors.

For instance, when we divide 2.5 by 3, the quotient is 0.83333333..., which has an infinite number of decimal places. Here, the product has more decimal places than the total number of decimal places in the factors.

Therefore, the number of decimal places in the product is not always the same as the total number of decimal places in the factors, and it depends on the specific mathematical operation being performed.

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Hey there! :)

Answer:

A. \(f(x) = (x - 2)^{4}\)

Step-by-step explanation:

Recall that the transformation form of a polynomial with degree four is:

\(f(x) =\) ±\(a(b(x-h))^{4} +k\)

In this instance, we will need to use the h value, or the horizontal shift.

It is given that there is only a horizontal shift of 2 units to the right, or h = 2. Plug this into the equation:

\(f(x) = (x - 2)^{4}\)

Approximately 95% of scores lie between -1.96 and 1.96 z-scores. This is because the area under the standard normal distribution curve between these two values is approximately 0.95.

To calculate this, first calculate the area under the standard normal distribution curve between -1.96 and 1.96. This can be done by using a Z-score table, which provides the area under the curve to the left of a given value. To calculate the area between -1.96 and 1.96, subtract the area to the left of -1.96 from the area to the left of 1.96. This is approximately 0.95.

Since the total area under the curve is 1, this implies that approximately 95% of scores lie between -1.96 and 1.96 z-scores. This is commonly known as the "95% Rule," and it is a useful way to quickly estimate the amount of scores that are within a certain range.

It is important to note that this calculation is only an approximation, as the exact value depends on the actual values that are used. Therefore, it is important to use a Z-score table with more accurate values if more precision is needed.

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Answer:

10x³ - 6x² - 9x + 12

Extra information:

★ Cubic polynomial: A polynomial of degree three is called cubic polynomial.

It is of the form P ( x ) = ax³ + bx² + cx + d [ Where a,b,c,d are real numbers and a is not equal to 0 . ]

Answer:

-11/3, -2.25, -3/2, 0.5

Step-by-step explanation:

We can use probability to find the answers to the questions - the final answers are given below.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

We will answer each part in detail.

Part (a)

No, there are more than 2 outcomes in this particular scenario.

Part (b)

Yes, there are two outcomes (Type A or not).

Part (c)

No, probability changes as the cards are dealt.

Part (d)

No, the trials are not independent.

Part (e)

Yes, two outcomes (more than 3 or not)

These are the final answers:

(a): No

(b): Yes

(c): Yes

(d): No

(e): Yes

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Answer:

64 inches tall

Step-by-step explanation:

We know in 1 foot, there are 12 inches.

We can convert 5 1/3 feet to 16/3 feet.

To do this you convert 5 feet to 15/3 feet and add it to 1/3 feet.

So we now have 16/3 feet and we will multiply by 12  to find the number of inches she is.

16/3 * 12 = 64 inches tall

A wardrobe with 3 pants, 5 shirts, and 7 ties, has a possible outcome of 105 outfits and not 15. So the answer is False

False. The number of total possible outfits is not 15. To calculate the number of possible outfits, we need to multiply the number of choices for each item together. In this case, we have 3 choices for pants, 5 choices for shirts, and 7 choices for ties. Therefore, the total number of possible outfits would be 3 x 5 x 7 = 105.

The statement incorrectly states that there are only 15 possible outfits. It's important to consider that when selecting multiple items, the total number of combinations is found by multiplying the number of choices for each item together. In this scenario, with 3 pants, 5 shirts, and 7 ties, there are 105 possible outfits, not 15.

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Answer:

∠ A = 70°

Step-by-step explanation:

The opposite angles in a cyclic quadrilateral are supplementary, then

∠ A + ∠ Q = 180°

∠ A + 110° = 180° ( subtract 110° from both sides )

∠ A = 70°

Answer:

11/12

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

Maximum number of bracelets Tara can make is 6.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

Tara has a plastic string that is 3 3/4 feet.

And, She will cut the string to make bracelets that are each 5/8 feet long.

Now,

To find maximum number of bracelets Tara can make, we can draw the point at equal distance 5/8 feet to reach 15/4 feet.

Then, Calculate the number of points to draw which is equal to the maximum number of bracelets Tara can make.

That is,

Maximum number of bracelets Tara can make = 15/4 ÷ 5/8

                                                                        = 15/4 × 8/5

                                                                        = 6

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The each base's length be 18 yards and 22 yards when a flower garden with a trapezoid shape is being planned by a landscaper.

Given that,

A flower garden with a trapezoid shape is being planned by a landscaper. She requests that the longer base be 7 yards longer than the height and that the shorter base be 3 yards longer. The flower garden is 150 square yards in size overall.

We have to find what will each base's length be.

We know that,

To be 3 yards longer than the height, the shorter base

b₁=h+3

To be 7 yards longer than the height, the longer base

b₂=h+7

Area of trapezoid=1/2(b₁+b₂)h

150=1/2(h+3+h+7)h

150=(2h+10)h/2

150=2h²+10h/2

150=2h²+5h

h²+5h-150=0

h²+15h-10h-150=0

h(h+15)-10(h+15)=0

(h-10)(h+15)=0

h=10 or h-15

h value should be positive.

So b₁=h+3=15+3=18

b₂=h+7=15+7=22

Therefore, The each base's length be 18 yards and 22 yards when a flower garden with a trapezoid shape is being planned by a landscaper.

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The coordinate of the point after a rotation of 90° counterclockwise will be (-3, -7).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The point is given below.

⇒ (-7, 3)

The coordinate of the point after a rotation of 90° counterclockwise will be given as,

(x', y') = (-y, x)

(x', y') = (-3, -7)

The coordinate of the point after a rotation of 90° counterclockwise will be (-3, -7).

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To determine whether the set s = {3 − 2t^2 t^3, −4 t^2, 2t t^3, 6t} is a basis for p3 (the vector space of polynomials of degree at most 3), we need to assess whether the vectors in s are linearly independent and whether they span p3.

To check for linear independence, we set up a linear combination of the vectors in s, equating it to the zero polynomial. By equating the coefficients of corresponding powers of t to zero, we can solve the resulting system of equations. If the only solution is the trivial solution (all coefficients are zero), then the vectors in s are linearly independent.

Next, we verify whether the vectors in s span p3. We need to determine if every polynomial of degree at most 3 can be expressed as a linear combination of the vectors in s. If for any polynomial in p3, we can find appropriate coefficients such that it can be expressed as a linear combination of the vectors in s, then s spans p3.

If the vectors in s are both linearly independent and span p3, then s forms a basis for p3. If either condition is not satisfied, s is not a basis for p3.

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Tt is proved that if ABCD is a parallelogram, then its opposite angles are equal.

So, the parallelogram angle theorem states that the opposite angles of a parallelogram are equal.

Therefore, we have A=C and B=D as it's proved that the opposite angles of parallelogram ABCD are equal.

Given: ABCD is a parallelogram.

To prove A=C and B=D, we need to prove parallelogram angle theorem.

Proof of Parallelogram Angle Theorem

Let's start the proof of parallelogram angle theorem:

In ΔACD and ΔCAB, we have

AC = AC (Common side)

AD = BC (Opposite sides of a parallelogram)

∠ACD = ∠CAB (Alternate angles)

Therefore, ΔACD ≅ ΔCAB (SAS congruence rule)

By CPCT, we have ∠A = ∠C

Similarly,

In ΔABD and ΔDCB, we have

BD = BD (Common side)AB = CD (Opposite sides of a parallelogram)∠ABD = ∠DCB (Alternate angles)

Therefore, ΔABD ≅ ΔDCB (SAS congruence rule)

By CPCT, we have ∠B = ∠D

Thus, it is proved that if ABCD is a parallelogram, then its opposite angles are equal.

So, the parallelogram angle theorem states that the opposite angles of a parallelogram are equal.

Therefore, we have A=C and B=D as it's proved that the opposite angles of parallelogram ABCD are equal.

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Answer: 19/30, 20/30, 21/30, 22/30, 23/30.

Answer:

Step-by-step explanation:

it is 2x