4. The parents made pies for the school bake sale to pay for the next field trip.
They made 55 apple pies and 45 blueberry pies. How many pies did they make
altogether? Estimate first, then solve.

Answer:

b.) 2

Explanation:

Given:

rewrite knowing 2⁵ = 32, (-2)⁵  = -32

simplify, ⁿ√xⁿ = x

distribute inside parenthesis

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$}[/tex]

The expression a/b ÷ c/d = ad/bc is A. true.

Given to show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc.

The ratio of two polynomials is an example of a rational expression. If an expression f is rational, it can be expressed in the form p/q, where p and q are polynomials.

Here we have a ,b ,c and d in the form of p/q form.

We take the reciprocal of the expression on the right side of the division sign when the rational expression a/b is to be divided by the rational expression c/d.

so, L.H.S = a/b ÷ c/d

= a/b × 1/(c/d)

= a/b × d/c

= ad/bc

= R.H.S

since L.H.S = R.H.S

a/b ÷c/d = ad/bc

Hence the expression a/b ÷ c/d = ad/bc is A.true.

Your question was incomplete. Please find the missing content here.

If A/B and C/D are rational expressions, then: A/B ÷C/D

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The only statement that holds for the given operation is Statement II

Given the following operartions

a [] b = a+b - ab/2

We need to check the true statement

For the expression x [] (y+z) =  x [] y +  x [] z

x [] (y+z) = x+y+z - x(y+z)/2

x [] (y+z) = x+y+z - (xy+xz)/2

x [] y +x [] z =  x+y - xy/2 +[x+z - xz/2 ]

x [] y +x [] z = x+y+x+z -xy/2 - xz/2

x [] y +x [] z = 2x+y+z - (xy+xz)/2

This shows that the statement I is incorrect

For the second statement

y [] z =  y+z - yz/2

x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2

x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4

For the other expression

x [] y =  x+y - xy/2

(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2

(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4

This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)

For the third statement

x [] z =  x+z - xz/2

y [] z =  y+z - yz/2

z [] 0 = z+0 - z(0)/2

z [] 0 = z

x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z

x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2

For the expression (x+y)[] z

(x+y)[] z = (x+y)+z - (xyz)/2

Hence the statement III is not valid

Based on the explanations above, the only statement that holds for the given operation is Statement II

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The determination of the money multiplier and the money supply for each reserve requirement listed in the following table are as follows:

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5                                          20                      $8,000

10                                           10                      $4,000

The money multiplier is the ratio of the reserve to the money supply.

The formula for determining the money multiplier is 1/r where r is the reserve ratio.

The money supply is the total amount of money circulating in the commercial banking system.

The quantity of the money supply is determined by multiplying the money multiplier by the total reserves.

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5                                    20 (1/0.05)               $8,000 ($400 x 20)

10                                     10 (1/0.1)                  $4,000 ($400 x 10)

Reserve Requirement    Simple Money     Money Supply

(percent)                             Multiplier             (Dollars)

  5

10

Thus, the money multiplier and money supply for the 5% reserve requirement are higher than for the 10% reserve requirement.

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[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

The lines shown below are perpendicular. Is this statement true or false?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

In order for a pair of lines to be perpendicular, they must intersect at a [tex]\bf{90^\circ}[/tex] angle. (a right angle)

[tex]\bf{Since\;the\;green\;line\;and\;the\;red\;one\;intersect\;at\;a\;right\;angle,}\\they\;are\;perpendicular.\\\\Hope\;you\;will\;have\;a\;fantabulous\;day!}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

A. sin θ = 5/8

Step-by-step explanation:

csc θ = 1/sin θ

csc θ = 8/5

1/sin θ = 8/5

sin θ = 5/8

Answer:

29 ft

Step-by-step explanation:

The distance along the ground from one stake to the tree, 21 ft, and the distance up the trunk from the ground, 20 ft, are the legs of a right triangle. The length of the wire is the hypotenuse of the right triangle. We can use the Pythagorean theorem to solve this problem.

a² + b² = c²

(21 ft)² + (20 ft)² = c²

c² = 841 ft²

c = √(841 ft²)

c = 29 ft

Answer: 29 ft

Each number in the sum is even, so we can remove a factor of 2.

2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)

Use whatever technique you used in (a) and (b) to compute the sum

1 + 2 + 3 + 4 + ... + 39 + 40

With Gauss's method, for instance, we have

S = 1 + 2 + 3 + ... + 38 + 39 + 40

S = 40 + 39 + 38 + ... + 3 + 2 + 1

2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41

S = 20×21 = 420

Then the sum you want is 2×420 = 840.

Answer:

down there

Step-by-step explanation:

we can see that angel rso and esk are congruent because they are verticle angels.

we also know that angel tse plus esk is equal to tsk, so angel tse+rso=tsk by algebra

Answer:

The correct answer is -14

Step-by-step explanation:

Answer:

11/15 < 4/5

Step-by-step explanation:

1.  5/6 = 10/12, so the first answer is not correct

2. 1/4 = 4/16, so the second answer is not correct

3. 3/4 = 9/12 and 4/6 = 8/12, so the third answer is not correct

4. 4/5 = 12/15 > 11/15, so this answer is correct

$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 10% and y represent the amount of money invested at a loss of 4%, hence:

x + y = 28500    (1)

Also:

(x * 1 year * 0.1) + (y * 1 year * -0.04) = 1310

0.1x - 0.04y = 1310   (2)

From equation 1 and 2:

x = 17500, y = 11000

$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.

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The liquid that will be the least dense liquid in the density column is; The  liquid floating on the top.

The formula for density is;

Density = Mass/Volume

Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.

Thus, this means that the liquid that is most dense will be at the bottom of the liquid.

The liquid that is least dense will be at the top of the liquid.

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The radius of the base is 8.245 cm

Given, a vase with a circular base exerts

Pressure = 700 N/m²

Force = 15 N

Area = ?

∴ area = πr²

By finding out the area of the vase we can calculate the radius.

We know that Pressure = Force/Area

According to the equation, pressure is inversely related to area but directly related to force. Pressure rises at a constant area as the force exerted increases in strength.

therefore apply the above the formula to find out the area and radius.

700 = 15/πr²

 πr² = 15/700

 πr² = 3/140

  r² = 3/140 × 3.14

since π value is 3.14

  r² = 0.0068

   r = √0.0068

   r = 0.0824 m

   r = 0.0824 × 100

   r = 8.245 cm

we get radius as 8.245 .

Hence we get the radius of the base of the vase as 8.245 cm.

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Answer:

5

Step-by-step explanation:

2x + 15 = 3x + 10

3x + 10 = 2x + 15

3x - 2x = 15 - 10

x = 5

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

[tex]2x + 15 = 3x + 10[/tex]

• Group like terms together:

  • Subtract 5 from both sides:

     [tex]2x = 3x - 5[/tex]

  • Subtract 3x from both sides:

      [tex]-x = -5[/tex]

• Multiply both sides by -1:

[tex]x = 5[/tex]  

Answer:

9 miles

Step-by-step explanation:

If 3 miles is equal to 15 mins

Then you do 3 miles and times by 3 cause if you times 15 by 3, you'll get 45 mins

So the answer= 9 miles

sinA+sinB+sinC

=2sin(A+B)/2cos(A-B)/2+sin C

=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2

=2cosC/2(cos(A-B)/2+cos(A+B)/2)

=4 cos A/2 cos B/2 cos C/2

= RHS

Answer:

c

Step-by-step explanation:

absolute values are positive and abs value of 0 = 0

The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

We have:

A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

Sample proportion = p = 378/504 = 0.75

q = 1 - p = 1 - 0.75 = 0.25

[tex]\rm SD = \sqrt{\dfrac{pq}{n}}[/tex]

[tex]\rm SD = \sqrt{\dfrac{0.75\times0.25}{504}}[/tex]

SD = 0.01928

For 95% confidence interval Z value = 1.96

Lower limit = 0.75 - 1.96(0.01928)

= 0.712

Thus, the lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.

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The correct statement regarding when the events will be independent is given as follows:

B. The probability of getting a red convertible is 0.06.

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this problem, the probabilities are given as follows:

The events will be independent if:

[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]

The intersection of events A and B is a red convertible car, hence the correct option is:

B. The probability of getting a red convertible is 0.06.

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By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.

In this question we must apply algebraic rules to find the roots of a quadratic equation, the roots are the values of the equation such that is equal to zero. Now we present the complete procedure:

6 · x² + 18 · x = 0

6 · x · (x + 3) = 0

x = 0 ∨ x = - 3

By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.

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Answer:

y = -19x + 14

Step-by-step explanation:

For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14

The expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.

Exponents are the base raised to a power, It is written in the superscript of a number.

The expression given in the statement can be written as

[tex]\rm \dfrac{ 2^{7/8}}{2^{1/4}}[/tex]

By the Exponent rule,

[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]

So the expression can be written as

=[tex]\rm 2^{5/8}[/tex]

=[tex]\rm \sqrt[8]{2^5}[/tex]

Therefore, in radical form, the expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.

The complete question is

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

2 to the 7 over 8 power, all over 2 to the 1 over 4 power

the eighth root of 2 to the fifth power

the fifth root of 2 to the eighth power

the square root of 2 to the 5 over 8 power

the fourth root of 2 to the sixth power

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The amount of stockholders’ equity as of August 31 of the current year is $26400.

The owner's equity will be:

= Cash + Supplies + Equipment - Account payable

= 27900 + 900 + 8500 - 7300

= 26400

Therefore, the amount of stockholders’ equity as of August 31 of the current year is

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Answer:

1.25 is the median for the first 12 days in January

Answer: {-3, -2, 1, 5}

Step-by-step explanation:

The domain is the set of x-values.

Answer:

Shirt: $45 , Tie: $12

Step-by-step explanation:

Let s be the price of the shirt

Let t be the price of the tie

Given the information from the question,

s + t = 57 - Equation 1

s - t = 33 - Equation 2

We will use substitution method to find the prices.

We will rearranging equation 1.

s = 57 - t

We will substitute s into equation 2.

57 - t - t = 33

57 - 2t = 33

-2t = 33 - 57

-2t = -24

t = -24 / -2

= 12

We now substitute t into Equation 1.

s + 12 = 57

s = 57 - 12

= 45

From here we know, the shirt costs $45 and the tie costs $12

The required value for the sum is 9580.

[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]

Simplification in mathematics to solve the given condition on its operators.

[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]

= [tex]\frac{10000}{1.028^2} +68*\frac{1-\frac{1}{1.028^2} }{\frac{0.115}{4} } \\9451+68*\frac{1-0.94}{\frac{0.115}{4} } \\\\9451+68*\frac{0.054}{\frac{0.115}{4} } \\\\\\9451+3.72{\frac{4}{0.115} } \\\\\\9451+129\\[/tex]

= 9580

The required solution is given as 9580.

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Answer:

significa que 1 barra de chocolate dividida entre 4 amigos es igual a 1 4. Por lo tanto, cada persona recibe 1 4 de la barra”. 6.

Step-by-step explanation:

Answer:

3/4 divided by 3 is 0.25

Step-by-step explanation:

We know that he has 3/4 of a candy bar and he wants to share it with himself plus 2 people.

The expression 3/4 divided by 3 represents this.

To change division to multiplication we use the reciprocal.

3/4 times 1/3 is 0.25.

Hope this helps. (:

Answer:

3x + y = 9.5

Step-by-step explanation:

1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.

y = -3x + c

2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.

-3 = 8 - k / k - 3

-3(k - 3) = 8 - k

-3k + 9 = 8 - k

-3k + k = 8 - 9

-2k = -1

k = -1/-2

k = 1/2

3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.

y = -3x + c

1/2 = -3(3) + c

1/2 = -9 + c

1/2 + 9 = c

9.5 = c

Completed equation of the line: y = -3x + 9.5

4) Write it in the form of ax + by = c.

3x + y = 9.5