D. 12:28
es 22. The label on a box of cereal states that it
contains 6 servings. If there are 7.5 cups in
the box, how many cups of cereal are there
per serving?

Since the function is h(t) = −5t² + 15t, the domain of the function h(t) is  0 ≤ t ≤ 3

The domain of a function is the range of input values that make the function have real values.

Now given the function h(t) = −5t² + 15t, it will have real values when

h(t) ≥ 0

So, h(t) ≥ 0

⇒  −5t² + 15t ≥ 0

Factorizing, we have

-5t(t - 3) ≥ 0

5t(t - 3) ≤ 0

t(t - 3) ≤ 0

t ≤ 0 and t - 3 ≤ 0

t ≤ 0 and t ≤ 3

For t ≤ 0, say -1, t(t - 3) = -1(-1 - 3) = -1(-4) = 4 ≥ 0

For 0 ≤ t ≤ 3, say 2, t(t - 3) = 2(2 - 3) = 2(-1) = -2 ≤ 0

For t ≥ 3, say 4, t(t - 3) = 4(4 - 3) = 4(1) = 4 ≥ 0

Since we require  t(t - 3) ≤ 0, the domain of t is thus 0 ≤ t ≤ 3

So, the domain of the function h(t) is  0 ≤ t ≤ 3

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Answer:

D) 96%

Step-by-step explanation:

If you take 96% of 28.6 you get 27.6 so it fits

Answer: 12/4

Step-by-step explanation: whole number = 3. given denominator = 4. 4/4 = 1. 1 times 3 = 3. 4 plus 4 plus 4 = 12. therefore answer is 12/4

Answer:

triangle PQR is similar to triangle TSR because the measure of angle 3 is congruent to the measure of angle 4 and the measure of angle one is congruent to the measure of angle 5

Step-by-step explanation:

angle 3 and angle 4 are congruent because they are vertical pairs.

Angles 1 and five are congruent because they are alternate interior angles

Considering the hypothesis tested, the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.

We fail to reject the null hypothesis, hence the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.

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The area of the kite exists 48 sq. ft.

The area of a kite exists half the outcome of the lengths of its diagonals. The formula to define the area of a kite exists:

Area = ½ × p × q.

Given that a kite contain diagonals of lengths 12 ft and 8 ft.

We know that the area of a kite having diagonals of length 'p' units and 'q' units exists

Area of kite = ½ (p × q)

Here, p = 12 ft and q = 8 ft.

Area of kite = ½ (p × q)

= (12 × 8)/2

= 96/2 = 48

Therefore, the area of the kite will be 48 sq. ft.

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The value of y in the triangle is B. 6✓3.

From the information given,

NU = 9

UM = 3

MN = 3 + 9 = 12

NT² = 9 × 12 = 108

NT = ✓108

NT = 6✓3

Therefore, y is 6✓3.

The value of y in the triangle is 6✓3.

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Answer:

B

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

140-80=60

Based on the triangle midsegment theorem, the midsegments and the sides they are parallel to are:

MP is parallel to XY

PZ is parallel to WX

MZ is parallel to WY

The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of the triangle. All triangles possess three midsegments. According to the triangle midsegment theorem, the third side of the triangle that is directly opposite the midsegment is twice the size of the midsegment and it is parallel to it.

In the diagram showing triangle WXY with midpoints at points M, Z, and P, the midsegments are:

MP which is parallel to XY, also, MP = 1/2(XY)

PZ which is parallel to WX, also, PZ = 1/2(WX)

MZ which is parallel to WY. also, MZ = 1/2(WY)

Thus, the midsegments and the sides they are parallel to are:

MP is parallel to XY

PZ is parallel to WX

MZ is parallel to WY

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The values of x and y that can represent the equation is illustrated.

The equation given us 32 = xy + 16

The table will be:

x. y

4. 4

16. 1

2. 8

32. 0.5

For example, when x and y are 4. This will be:

= xy + 16

= (4 × 4) + 16

= 32

Other values of x and y will also give 32.

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Answer:

Median

Explanation:

Real estate prices are virtually usually biased to the right. If we estimate the price of a typical home in a city at $500,000. We would have no trouble locating properties for $2 million and $3 million, and perhaps even some $5 or $6 million residences. However, you won't find houses for under $1.5 million. Because of this, the mean value is pulled toward the high end more than the median value.

Step-by-step explanation:

find the greatest number which divides 225 and 1029 leaving remainder of 5 in each case

Answer:

x = 15 & y = 35

Step-by-step explanation:

[tex]y = x + 20[/tex]

[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]

[tex]y = x + 20 = (15) + 20 = 35[/tex]

The area of the circular manufactured good is given by:

[tex]A = 1.8146 \times 10^{16} \text{m}^2[/tex]

The area of a circle of radius r is:

[tex]A = \pi r^2[/tex].

In this problem, the radius in meters is:

[tex]r = 7.6 \times 10^7[/tex]

Hence the area in m² is:

[tex]A = \pi (7.6 \times 10^7)^2 = 181.46 \times 10^{14} = 1.8146 \times 10^{16} \text{m}^2[/tex]

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From ratio concept, the greater number number is 32 .

A ratio exists as an ordered pair of numbers a and b, written a / b where b does not equivalent to 0. A proportion exists in an equation in which two ratios stand set equal to each other. For example, if there exists 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there exist 3 girls)

Let the greater number be x .

The ratio given is 3:8 .

Thus, by the concept of ratio -

⇒ 3/8 = 12/x

⇒ x = (8/3 * 12)

∴  x = 32

Therefore, from ratio concept, the greater number number is 32 .

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Answer:

x = 70

Step-by-step explanation:

x and 2x - 30 are supplementary angles , sum to 180° , then

x + 2x - 30 = 180 ( add 30 to both sides )

3x = 210 ( divide both sides by 3 )

x = 70

Answer:

2x - 30 and x degrees should add up to 180 degrees

2x - 30 + x = 180

3x = 210

x = 70 degrees

The correct answer would be D

Based on the information given about the equation, y will be 0.5x + 2.

From the information given, it should be noted that the equation of the line it represents was given and the y intercept is = (0, 2).

The function to represent y will be:

y = mx + b

y = (1/2)x + 2

y = 0.5x + 2

In conclusion, y = 0.5x + 2.

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Answer: A

Step-by-step explanation:

The polynomial has roots at [tex]x=-4, -2, 4[/tex].

So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].

This eliminates everything except for A.

The total interest is $107,270

What is monthly payment formula?

The formula for monthly payment is:

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

We can find total interest as shown below:

Value of property = $475,000

Money available as a deposit = $80,000

P = 475,000-80,000

= 395000

t = 25 year

r = 2% = 0.02

n = 25*12 = 300

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

Putting the value of P, t, r, and n in the above formula

[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]

after solving the above expression

M = $1674.22

Interest = M*n-P

Putting the value of P, n and M

= 1674.22*300-395000

= 502266-395000

= 107,266

Rounding to nearest ten dollar

= $107,270

Hence, the total interest is $107,270.

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Answer:

Step-by-step explanation:

Factorization implies the obtaining of the common factors in an expression.

The term factorization implies the obtaining of the common factors in an expression.

The factors of the expressions are as follows;

1) (x−1)(x+7)

2) (x−2)(x−3)

3) (x+1)(x−7)

4) (x−1)(x+6)

5) (x−3)(x+4)

6) (x+2)(x−4)

7) (x+1)(x−5)

8) (x−1)(x+3)

9) (x+4)(x−4)

10) (x+3)(x−4)

11) (x−3)(x−6)

12) (x+2)(x−7)

13) (x−2)(x−5)

14) (x−3)(x−8)

15) (x+5)(x−6)

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The polynomial function is P(x) = x^3(x + 1)^3(x -1)

The zeros of the polynomial and the multiplicities are given as:

The degree is given as

Degree = 7

The polynomial is represented as:

P(x) = (x - zero)^multiplicity

Using the above format, we have

P(x) = (x + 1)^3(x - 0)^3(x -1)

This gives

P(x) = x^3(x + 1)^3(x -1)

Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)

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The function P(x), for the price of the materials for the pen is 4.18(800/x + x) + 38.

Based on the information, the function P(x), for the price of the materials for the pen will be:

P(x) = 4.18 (2 × 400/x + x) + 38

= 4.18(800/x + x) + 38.

The dimensions will be:

We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.

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Answer:

The water costs $1.90, the chips are $.95 and the milk is $3.80.

Step-by-step explanation:

Let m = milk

Let w = water

Let c = chips

2m+6w+7c =25.65      w = 2c     m = w + 1.90

For the first equation, substitute w for 2C and m for w + 1.90 to get:

2(w+1.90) +6(2c) + 7c = 25.65

2w+3.8+12c+7c=25.65

2w+19c = 21.85

Now substitute 2c for w:

2(2c)+19c =21.85

4c + 19c = 21.85

23c = 21.85

c = .95  Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.

w = 2c

w=2(.95) = 1.90

m = w + 1.90 = 1.90+1.90 = 3.80

Option A, The option that has the same potential roots according to the rational root theorem is 3x5 – 2x4 – 9x3 + x2 – 12.

We have p, this is the factors of the number 12.

The factors are ±(1, 2, 3, 4, 6, 12)

We have factors of q = 3

= ±(1, 3)

The rational roots are the roots that have the same factors that are contained in the question.

Hence the answer is A.

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Answer:

The Answer is A

Step-by-step explanation:

Did it on edge :)

Therefore, the bones were 6612.5 years old at the time they were discovered.

Given that the radioactive element​ carbon-14 has a​ half-life of 5750 years, and a scientist determined that the bones from a mastodon had lost 57.5​% of their​ carbon-14, to determine how old were the bones at the time they were discovered, the following calculation must be made:

Therefore, the bones were 6612.5 years old at the time they were discovered.

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Answer:Therefore, the bones were 6612.5 years old at the time they were discovered.

Step-by-step explanation:

The equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]

The natural logarithm equation is given as:

ln 5 = y

Rewrite as:

ln(5) = y

Take the exponent of both sides

[tex]e^{ln(5)} = e^y[/tex]

Evaluate the expression

[tex]5 = e^y[/tex]

Rewrite as:

[tex]e^y = 5[/tex]

Hence, the equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]

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Using it's concept, it is found that there is a 27.3% probability that someone throws the 11-sided die one time and rolls a number 9 or higher.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 11 numbers, 3 of which are 9 or higher, hence the probability is:

p = 3/11 = 0.273 = 27.3%.

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They don't need to be pure real or imaginary. Any "mixed" complex number works so long as [tex]z=z'[/tex].

Let [tex]z=z'=a+bi[/tex]. Then

[tex]|z+z'| = |2a+2bi| = 2 \sqrt{a^2+b^2}[/tex]

[tex]|z| + |z'| = 2|a+bi| = 2 \sqrt{a^2+b^2}[/tex]

so [tex]|z+z'|=|z|+|z'|[/tex].

The geometric interpretation is essentially identical. [tex]|z+z'|=2|z|[/tex] is a complex number twice the distance away from the origin in the complex plane as [tex]z[/tex], which is exactly [tex]|z|+|z|[/tex].

The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.

Notice that the Angles of a Triangle add up to 180° That is

∠A + ∠B  + ∠C = 180°

Thus,

∠C = 180° - 32° - 109°

= 39°

Recall the Sine Theorem which indicates;

a/SinA = b/SinB = c/SinC

thus given that

AC = 1,523m

We have

AC/SinB = BC/SinA

BC = AC/SinB * SinA

= 1523/Sin109° * Sin32°

BC =854m

Therefore

AC/SinB = AB/SinC
Thus,

AB = AC/SinB * SinC

= 1523/Sin109° * Sin39°
AB ≈ 1,014m

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