Dana is buying Grandparents' Day gifts at the mall. She spends $13.75 on a teacup for her grandmother. She spends 4/5 of that on a coffee mug for her grandfather. How much money does Dana spend in all?

The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

Note that:

f(t)= 50 (1/2)^ [tex]\frac{t-2}{5}[/tex]

f(t)= 50 (1/2)^ [tex]\frac{\frac{t}{5} } - {\frac{2}{5} }[/tex]

Note also that in indices,  [tex]x^{-y}[/tex] = 1/ [tex]x^{y}[/tex]

Then:  50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

([tex]50 \frac {1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

= 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

Therefore, The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])

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The solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression will be solved as follows:-

E =  [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]

E = [tex]\sqrt{7\times 7\times 3\times xy^7\times x^5y^5[/tex]

E=[tex]\sqrt{7\times 7\times 3\times x^6y^{12}[/tex]

E = 7x³y⁶√3.

Therefore the solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.

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Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.

What is Pythagoras Theorem?

The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.

The formula for Pythagoras Theorem is given by,

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

Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.

Each Subtraction in view of Pythagoras Theorem

It is is given that,

[tex]d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

or  [tex]d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}[/tex]

Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.

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Work Shown:

[tex]1.04 \cdot 10^4 + 5.6 \cdot 10^2\\\\10,400 + 560\\\\10,960\\\\1.096 \cdot 10^4\\\\[/tex]

Note: Something like [tex]5.6 \cdot 10^2[/tex] means we move the decimal point two spots to the right to get to 560. If the exponent was negative, then we move that many spaces to the left.

The sample size required to estimate the fraction of people who are captured after appearing on the 10 most wanted list is 228.

Given  standard deviation of 0.26 ,margin of error of 0.04, and confidence interval of 98%.

We have to determine the sample size required to estimate the fraction of people who are captured after appearing on the 10 ost wanted list.

We can find the sample size with the help of margin of error.

Margin of error is the difference between the calculated values and real values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where σ is standard deviation,

n is sample size and z is critial z value.

We have to find the z value for 98% confidence level from z table.

z value=2.326.

Put the values in the formula of margin of error.

0.04=2.326*0.26/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=2.326*0.26/0.04

[tex]\sqrt{n}[/tex]=15.119

squaring both sides we get

n=228.58

By rounding we get

n=228.

Hence the sample size needed is 228.

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Clara is 15 years old, and there are 120 coins on the box.

Each year her mom puts as many coins in her money box as how old she turns that day.

So on her first birthday, 1 coin is put in the box.

On her second birthday, 2 coins are put in the box

And so on.

So we have the simple summation:

[tex]\sum_{n = 1} n[/tex]

We know that the outcome of that summation is a number in the interval [110, 130]

If we know that the sum goes from n = 1 to n = N (N is the age of Clara) then we can rewrite the summation as:

[tex]N*(N + 1)/2[/tex]

Now we can solve:

[tex]N*(N + 1)/2 = 110\\\\N^2 + N = 220\\\\N^2 + N - 220 = 0[/tex]

The two solutions of the quadratic equation are:

[tex]N = \frac{-1 \pm \sqrt{1^2 - 4*1*(-220)} }{2} \\\\N = (-1 \pm 29.7) /2[/tex]

If we take only the positive solution:

N = (-1 + 29.7)/2 = 14.35

Now, notice that we got this number by taking the smallest possible number of coins (110) So we can round this to the next whole number, which is 15.

If N = 15, then the number of coins in the box is:

15*(15 + 1)/2 = 120

Which lies on the wanted interval.

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Answer:

In a class of 40 students, 20% are females. How many males are in the class?​

ANSWER

= 32

if in a class of 40 students 20% are females that means 80% of the class are males...

The equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0

A polynomial is an algebraic equation with at least the power of its variable 3.

Analysis:

if -2, -6, -10i are the zeroes of the polynomial, it means x = -2, x = -6, x = -10i

if x = -2, (x+2) is a factor, (x+6) is a factor.

convert x = -10i to a real number,

i = [tex]\sqrt{-1}[/tex]

-10[tex]\sqrt{-1}[/tex] = 10[tex]\sqrt{- -1}[/tex] = 10[tex]\sqrt{1}[/tex] = 10

x = 10, so (x-10) is a factor.

Therefore equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0

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Answer:

[tex]\huge\boxed{\sf 2a^2-13b^2+12abc}[/tex]

Step-by-step explanation:

[tex]=6a^2-4b^2+4abc-9b^2-4a^2+8abc\\\\Combine \ like \ terms\\\\=6a^2-4a^2-4b^2-9b^2+8abc+4abc\\\\=2a^2-13b^2+12abc\\\\\rule[225]{225}{2}[/tex]

Answer:

Hello! The answer is: [tex]2a^2 - 13b^2 + 12abc[/tex]

Step-by-step explanation:

[tex]6a^2 - 4b^2 + 4abc - 9b^2 - 4a^2 + 8abc[/tex]

Rearrange to combine like terms:

[tex]6a^2 - 4a^2 - 4b^2 - 9b^2 + 4abc + 8abc[/tex]

Combine like terms:

[tex]2a^2 - 13b^2 + 12abc[/tex]

Answer:

y = x + 4

Explanation:

Initially (at week 0) = 4 cases

now (at week 1) = 5 cases

now (at week 6) = 10 cases

turn them into points:

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{5-4}{1- 0 } = 1[/tex]

Find equation:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf \rightarrow y-4 =1(x -0)[/tex]

[tex]\sf \rightarrow y = x +4[/tex]

Answer: 1.65

Step-by-step explanation:

     First, we must find 8/25 of 1.25. This is using multiplication.

1.25 * 8/25 = 0.4

    Now, we can increase 1.25 by 8/25 of it. This is using addition.

1.25 + 0.4 = 1.65

The given statement can be modeled as an algebraic expression (3m+7)/27 < n.

In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The statement is given as "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression.

(3m+7)/27 < n

Hence, the given statement can be modeled as an algebraic expression (3m+7)/27 < n.

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Answer: =2x²y³+3y.

Step-by-step explanation:

[tex]\frac{14x^5y^4+21x^3y^2}{7x^3y} =\frac{7x^3y*(2x^2y^3+3y)}{7x^3y}= 2x^2y^3+3y.[/tex]

hard to tell but from 0.75 to 1

60 × 48 = 2880 L

2880 ÷ 700 = 4

Answer:

20  1 Liter Cartons

40  700 ml Cartons

Step-by-step explanation:

Let A be the number of 700ml cartons.

Let B be the number of 1 L cartons

We are told that A + B = 60 cartons total

Rearrange to isolate A:  A = 60 - B

700ml is 0.700L

Total volume of milk is 48L

Total volume (in liters) of the 700 ml cartons is from (0.70 L)A

Total volume from the 1L cartons is (1 L)B

Total = (0.70)A + 1B = 48 L

Now use the rearranged equation for A in the above espression:

(0.70)A + 1B = 48 L

(0.70)(60-B) + 1B = 48 L

42 - 0.70B + B = 48

0.30B = 6

B = 20

A is 60 - B or 40

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

CHECK:

B:  20*(1 L)       = 20 L

A:  40*(0.70 L) =  28 L

Total =                   48 L  YES

Answer:

0.035

Step-by-step explanation:

Since all of them find a job, the probability is

[tex]51\%\times51\%\times51\%\times51\%\times51\%\\\\=(51\%)^5\\\\=0.035[/tex]

(rounded to the nearest thousandth)

Using relations in a right triangle, it is found that:

tan(A) = 3/4 = 0.75.

The relations in a right triangle are given as follows:

In this triangle:

Hence the tangent of A is:

tan(A) = 30/40 = 3/4 = 0.75.

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Work Shown:

i = P*r*t

i = 1250*0.045*5

i = 281.25

Answer:

x=2 or x= -1

Step-by-step explanation:

when  f(x) = 0

⇒| 2x-1 | =3

case(i)  (x>1/2)

2x-1=3

x=2

case(ii) (x<1/2)

-(2x-1)=3

2x-1=-3

x=-1

case(iii) (x=1/2)

[tex]0=3[/tex] absurd.

Answer:

Step-by-step explanation:

If a boat can travel 408 miles on 204 gallons, this means that for every 2 miles, it requires 1 gallon.

So, for 169 gallons, there are 2 miles for every gallon.

So, multiply 169 * 2.

The answer is 338

Hope this helps!

Answer: O253

Step-by-step explanation:

The correct expression which represents the volume of the cone is,

V = 2x³π/3

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The height of a cone is twice the radius of its base.

Let radius of cone = x

Then, The height of cone = 2x

Hence, The volume of cone is,

V = 1/3πr²h

V = 1/3 × π × x² × 2x

V = 2x³π/3

Thus, The correct expression which represents the volume of the cone is,

V = 2x³π/3

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The value is P(p'-p > 0.17) = 0.09

From the question we are told that

The population proportion is p=0.19

The sample size is n = 479

Generally given that the sample size is large enough , i.e  n > 30 then the mean of this sampling distribution is mathematically represent

[tex]u_{x} =p=0.19[/tex]

Generally the standard deviation is mathematically represented as

σ[tex]=\sqrt{ \frac{p(1-p)}{n}[/tex]

σ= [tex]\sqrt{ \frac{0.19(1-0.19)}{479}[/tex]

σ=0.017

Generally the the probability that the sample proportion will differ from the population proportion by greater than 17% is mathematically represented as

[tex]P(p'-p > 0.17) =P (z > \frac{0.17}{0.017} )[/tex]

[tex]P(p'-p > 0.17) =P (z > 10 )[/tex]

[tex]P(p'-p > 0.17) =P (z > 10 ) - P (z > -10 )[/tex]

From the z table  the area under the normal curve to the left corresponding to 10  and - 10 is

[tex]P(p'-p > 0.17) = 0.97042 - 0.87450\\P(p'-p > 0.17) = 0.09[/tex]

So, the value of probability is greater than 17% is P(p'-p > 0.17) = 0.09

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The probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.

The true proportion of the sample or the mean of the sample = 19%, that is, μ = 19% or 0.19.

The sample size (n) = 479.

The sample proportion is to be calculated at the point 17% or 0.17.

The standard error (s) = √{μ(1 - μ)/n} = √{0.19(1 - 0.19)/479} = 0.0179.

We are asked to calculate the probability that the sample proportion is greater that 17% or 0.17.

This is written as P(X > 0.17) = P(Z > {(0.17-0.19)/0.0179}) = P(Z > -1.1173) = 1 - P(Z ≤ -1.1173) = 1 - 0.1304 = 0.8696 or 86.96%.

To calculate this using the calculator, we use the calculator function:

Normalcdf(0.17,10000000,0.19,0.0179) = 0.8677 or 86.77%.

Thus, the probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.

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Answer:

1/3

Step-by-step explanation:

please mark brainliest if correct

Answer:

215 is the answer of the 2 triangles

Answer: Yes because of ASA or AAS (C)

Step-by-step explanation:

Got it right on edge ")

Answer:

0.291×0.34=0.09894

Answer:  0.09894

We are going to use long division: