Which is the equivalent expression of 78?
2 × (10 × 3 + 32)
2 × (13 + 32)
(10 × 3 + 32)
2 × (10 × 3 + 3)

Answer:

[tex]y^{5}[/tex] + 11y³ - 2y² - 22

Step-by-step explanation:

(y³ - 2)(y² + 11)

each term in the second factor is multiplied by each term in the first factor.

y³(y² + 11) - 2(y² + 11) ← distribute both parenthesis

= [tex]y^{5}[/tex] + 11y³ - 2y² - 22

Answer:

mean: 2.6, mode: 1, median: 1

Step-by-step explanation:

The mean is essentially the average of the data set which can be defined as: [tex]\frac{\text{sum of data set}}{\text{amount of data in data set}}[/tex]. So adding all the values together you get: [tex]26[/tex]. and counting all the numbers in the data set you find the data set has 10 numbers. This gives you the equation: [tex]\frac{26}{10} = 2.6[/tex] which is the mean

To find the mode, you find which number occurs most frequently, this is of course 1, which can really be determined by just looking at the data set for a second. all the other numbers only occur once, while 1 is in the data set 5 times. So 5 is the mode

To find the median you sort the data, from min to max, and then find the middle number. Sorting the data set gives you. -2, 1, 1, 1, 1, 1, 4, 5, 6, 8. Since this data set has an even amount of numbers, there is not going to be an exact middle. If you go the "middle" which is the 5th and 6th number, you add these two numbers and divide the sum by 2. This gives you: (1+1)/2 = 1 So the median is 1

Answer:

Let the cost price be x

[tex]\rm{C.P. = \dfrac{S.P. \times 100}{100+ gain \% }}[/tex]

[tex]\rm{C.P. = \dfrac{130 \times 100}{100+30}}[/tex]

[tex]\rm{ C.P. = \dfrac{130}{30} }[/tex]

[tex]\large{\boxed{\rm{ C.P. = \dfrac{13}{3}}}}[/tex]

Answer:

[tex] \boxed{\bf A. \: x - 2}[/tex]

Step-by-step explanation:

[tex] \sf ( x + 1)^2-9/ x + 4 [/tex]

First, we need to factor the expressions that are not already factored.

Now, let's Cancel out x+4 in both numerator and denominator.

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

Answer:

a = 2

Step-by-step explanation:

given x = - 1 is a zero then f(- 1) = 0 , that is

a(- 1)³ - (- 1)² - 1 + 4 = 0

- a - 1 - 1 + 4 = 0

- a + 2 = 0 ( subtract 2 from both sides )

- a = - 2 ( multiply both sides by - 1 )

a = 2

The options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

From the figure,

The interior angle of a triangle is w

w > x (true)

w > y (true)

x + y = w (sum of the two interior angles is equal to the exterior angle)

Thus, the options w > x, w > y, and x + y = w are correct because the sum of the two interior angles is equal to the exterior angle.

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Considering the given probability distributions, distribution D is valid.

A probability distribution is valid if:

In this problem, only distribution D has a sum of 1, hence it is the only valid distribution.

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Answer:

Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.

Step-by-step explanation:

The answer above is correct.

The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.

Sample size (n) = 16.

Sample mean = 2.8 minutes.

Sample standard deviation (σ) = 1.2 minutes.

Confidence interval given = 95%.

The degree of freedom (df) can be calculated as n - 1.

df = n - 1 = 16 - 1 = 15.

Since, the level of confidence is 95%, the level of significance α = 1 - 0.95 = 0.05.

From the T-Distribution table, we take the value at critical value α/2 with the degree of freedom 15.

[tex]t_{\frac{\alpha }{2} ,15}[/tex] = 2.131.

Now, the margin of error can be shown as follows:

[tex]E = t_{\frac{\alpha }{2} ,15} * \frac{\sigma}{\sqrt{n} } \\\Rightarrow E = 2.131 * \frac{1.2}{\sqrt{16} }\\ \Rightarrow E = 0.6393[/tex]

The width at the confidence interval of 95%, is twice the margin of error, that is:

Width = 2*E = 2*0.6393 = 1.2786.

Thus, the width (in minutes) of the 95 percent confidence interval for the true mean transaction time is 1.2786 minutes.

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Answer: ∠PQR = 130°

Step-by-step explanation:

      The word bisects means that angle PQS and SQR are equal to each other.

           3x + 5 = 2x + 25

           3x = 20

           x = 20

      Now, we will plug this value back in and solve for angle PQR. There are three ways we could do this.

      [1]

             (3x + 5) + (2x + 25)

             (3(20) + 5) + (2(20) + 25)

             (60 + 5) + (40 + 25)

             (65) + (65)

                 130 degrees

      [2]

             (3x + 5) * 2

             (3(20) + 5) * 2

             (65) * 2

                 130 degrees

      [3]

             (2x + 25) * 2

             (2(20) + 25) * 2

             (65) * 2

                 130 degrees

Answer:

C

Step-by-step explanation:

you know the drill

[5] No slope (or a slope of 0)

      There is no incline or decline to the line, so there is no slope.

[6] 1

      We can use "rise over run" since we have clear points on the graph. See attached.

[7] Undefined slope

      This slope of this line is undefined. The formula for slope is [tex]\frac{\text{change in y}}{\text{change in x}}[/tex] which becomes [tex]\frac{0}{0}[/tex] in a case like this. You cannot divide by 0, giving a slope of undefined.

Answer: A. X = -1

Step-by-step explanation:

An axis of symmetry is the line that divides the object into two equal halves, creating a mirror-like reflection. Only at x = -1 will that occur.

[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]

★ Radius of first sphere [tex]\sf r_{1}[/tex] = 6cm.

★ Radius of second sphere [tex]\sf r_{2}[/tex] = 8cm.

★ Radius of third sphere [tex]\sf r_{3}[/tex] = 10cm.

[tex] {\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]

★ The radius of the resulting sphere formed.

[tex] {\large{\textsf{\textbf{\underline{\underline{Formula \: used :}}}}}}[/tex]

[tex]\star \: \tt Volume \: of \: sphere = {\underline{\boxed{\sf{\red{ \dfrac{ 4}{3}\pi {r}^{3} }}}}}[/tex]

[tex] {\large{\textsf{\textbf{\underline{\underline{Concept :}}}}}}[/tex]

★ As, three spheres are melted to from one new sphere. Therefore, volume of three old sphere is equal to volume of new sphere.

i.e, Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.

[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

Let,

The radius of resulting sphere be [tex]R[/tex]

According to the question,

• Volume of first sphere + volume of second sphere + volume of third sphere = Volume of new sphere.

[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(r_{1})}^{3} + \dfrac{4}{3} \pi {(r_{2})}^{3} + \dfrac{4}{3} \pi {(r_{3})}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]

• here

☆[tex]\: \sf r_{1}[/tex] = 6cm

☆[tex]\: \sf r_{2}[/tex] = 8cm

☆[tex]\: \sf r_{3}[/tex] = 10cm

Putting the values,

[tex] \longrightarrow \sf \dfrac{4}{3} \pi {(6)}^{3} + \dfrac{4}{3} \pi {(8)}^{3} + \dfrac{4}{3} \pi {(10)}^{3} = \dfrac{4}{3} \pi {(R)}^{3} [/tex]

Taking " [tex]\dfrac{4}{3} \pi [/tex]" common,

[tex] \longrightarrow \sf \dfrac{4}{3} \pi \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \dfrac{4}{3} \pi {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \cancel{ \dfrac{4}{3} \pi} \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = \cancel{ \dfrac{4}{3} \pi } {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \bigg[ {(6)}^{3} + {(8)}^{3} + {(10)}^{3} \bigg] = {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \bigg[ 216 +512 + 1000 \bigg] = {(R)}^{3} [/tex]

[tex]\longrightarrow \sf 1728 = {(R)}^{3} [/tex]

[tex]\longrightarrow \sf \sqrt[3]{1728} = R[/tex]

[tex]\longrightarrow \sf \sqrt[3]{ 12 \times 12 \times 12 } = R[/tex]

[tex]\longrightarrow \sf \sqrt[3]{ {(12)}^{3} } = R[/tex]

[tex]\longrightarrow \sf R = \red{12 \: cm} [/tex]

Therefore,

Radius of the resulting sphere is 12cm.

[tex]{\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}[/tex]

★ Figure in attachment.

[tex]{\underline{\rule{290pt}{2pt}}}[/tex]

Answer:

b = 23.3

Step-by-step explanation:

First, we need to determine whether this is a right or non-right triangle.

We know that the sum of all the angles in a triangle must add up to 180, so we can add angles A and B and subtract the sum from 180:

[tex]180-(40+88)=180-128=52[/tex]

The 52 indicates that it is a non-right triangle, so we must rely on either the law of sines or law of cosines to find the measure of b.

Given that we have angle A and its resulting side, a, along with angle B, we can use the law of sines:

[tex]\frac{sin A}{a}=\frac{sin B}{b}[/tex]

[tex]\frac{sin 40}{15}=\frac{sin 88}{b}\\ \\ 15*sin 88=b * sin 40\\\\b=\frac{b*sin 40}{sin 88}\\ \\b=23.3216=23.3[/tex]

Answer:

(r,0)

Step-by-step explanation:

Answer:

Given that,

Maira has a total of Rs.1040 as currency notes in the denomination of Rs.10, Rs.20 and Rs.50.

The ratio of the number of Rs.10 notes and Rs.20 notes is 2:5.

She has a total of 30 notes with her.

Let assume that

Number of Rs 10 notes be 2x

Number of Rs 20 notes be 5x

Number of Rs 50 notes be 30 - (2x + 5x) = 30 - 7x

So,

[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad\sf \:Denomination \: of \: Rs \: 10=2x\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=5x\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=30 - 7x\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]

Now,

Amount in form of Rs 10 = 10 × 2x = Rs 20x

Amount in form of Rs 20 = 20 × 5x = Rs 100x

Amounts in form of Rs 50 = 50 × (30 - 7x) = Rs 1500 - 350x

Now, According to statement

[tex]\begin{gathered}\sf \: 20x + 100x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 120x + 1500 - 350x = 1040 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \: 1500 - 230x = 1040 \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\sf \:- 230x = - 460 \\ \\ \end{gathered}[/tex]

[tex]\sf \: \implies x = 2 [/tex]

Hence,

[tex]\begin{gathered}\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Denomination \: of \: Rs \: 10=4\qquad \: \\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 20=10\\ \\& \qquad \:\sf \: Denomination \: of \: Rs \: 50=16\end{aligned}} \qquad \\ \\ \end{gathered}[/tex]

Answer: 25.6

Step-by-step explanation:

[tex](d-3) \tan 37^{\circ}=17\\\\d-7=\frac{17}{\tan 37^{\circ}}\\\\d=\frac{17}{\tan 37^{\circ}}+3 \approx \boxed{25.6}[/tex]

Answer:

x = 6, y = 5

Step-by-step explanation:

5x - 4y = 19 -------> equation 1

x + 2 = 8 --------> equation 2

Step 1 : Subtract 2 on both sides in equation 2.

x + 2 - 2 = 8 - 2

x = 6

Step 2 : Substitute the value of x is equation 1.

5 ( 6 ) - 4y = 19

( 5 * 6 ) - 4y = 19

30 - 4y = 10

Step 3 : Subtract 30 on both sides.

30 - 30 - 4y = 10 - 30

- 4y = - 20

Step 4 : Multiply - 1 on both sides.

- 1 * - 4y = - 1 * - 20

4y = 20

Step 5 : Divide 4 on both sides.

4y / 4 = 20 / 4

y = 5

Hence,

x = 6

y = 5

Answer:

x = 5, y = 3/2.

Step-by-step explanation:

5x-4y=19

x+2y =8               Multiply this by 2:

2x + 4y = 16       Adding this to first equation 1:

7x = 35

x = 5

So

5 + 2y = 8

2y = 3

y = 3/2.

Answer:

Hence the expression [tex]$$(6p+5)(p+1)=6p^2+11p+5$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ \times & {} & p & + & 1 \\ \end{matrix}}[/tex]

_____________

[tex]{\frac{\begin{matrix}{} & {} & 6p & + & 5 \\ 6{{p}^2} & + & 5p & {} & {} \\ \end{matrix}}{\begin{matrix}6{{p}^2} & + & 11p & + & 5 \\ \end{matrix}}}$$[/tex]

Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours -> They drove a total of 55 x 3 = 165 miles.

After lunch, they drove at a constant rate of 45 miles per hour for 2 hours -> They drove a total of 45 x 2 = 90 miles.

So, the total amount of miles the Ramos family drove is 165 + 90 = 255 miles.

Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours.

[tex]\longrightarrow \tt{55*3=165}[/tex]

After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.

[tex] \longrightarrow \tt{45*2=90}[/tex]

Total miles the Ramos family drive

[tex] \longrightarrow \tt{165+90=255}[/tex]

[tex]answer : \pink{255} \: \tt{miles}[/tex]

Answer:

d≈9.55

Step-by-step explanation:

the answer is 9.55 inches

Answer:

diameter = 9.55 in

Step-by-step explanation:

Circumference = pi x diameter     so re-arrange

circumference / pi = diameter

       30 / pi = diameter

   9.55 in = diameter

Answer: 80 miles

Step-by-step explanation:

- 400/5 = 80

- so 80 is 1/5 of 400

hope this helps :)

Answer:

80 miles

Step-by-step explanation:

The whole journey is 400 miles, so we say that he traveled x miles, where x equals 400.
if we multiple 1/5 by x miles, then we will get how much he travels
1/5*x = 1/5*(400), since x = 400, so you can replace x with 400
1/5*x=1/5*400=400/5=80 miles

Answer:

C

Step-by-step explanation:

When x is negative    1/2 ^x  becomes   1 / ( 1/2 ^x)   meaning it is quite large as x becomes more negative

   when x = 0  the value is 1  

  as x increases from 0 to + inf   the value becomes smaller...but never negative

   the only graph that fits is C

The graph is concave has two curved part as follows;

The direction the concave part of the graph faces is given as follows;

The graph is concave up when the concave part faces up

It is concave down when the concave part faces down

From the given diagram, we have;

The graph is concave up between;

(0, 1), and (1, 0)

The graph is concave down between; (0, 1), and (-a, 2)

Where a is in the range; 1 < a < 2

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Answer:

So now,

you know the formula for simple interest is P×R×T divided by a hundred?

So 2500 times 3.55 times 2.75 divided by 100

Given :

Subtract 5 from each side :

Take the root on each side :

Hence, the values of x are :

[tex]x^2+5=6\\x^2=1\\x=1 \vee x=-1[/tex]

A = {x|x ∈ U and is an even positive integer}

The universal set(U) consists of only positive integers.

Given,  A = {x|x ∈ U and x is an odd positive integer}.

That means the set A contains all those elements which belongs to the universal set and should be a positive odd number.

refers to the complement of A. It means that it will contain all those elements that belong to U but does not belong to A.

All  the positive odd integer is made up of two types of number ,i.e, positive and negative number.

So,this set will contain all the element belonging to U and should be an even positive integer.

Therefore,Ac = {x|x ∈ U and is an even positive integer}.

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Answer:D:Ac = {x|x ∈ U and is an even positive integer}

Step-by-step explanation:

edge 2022

The system of equations representing these costs are; y = 7.5x and y = 5.5x + 10

The slope of the first line is;

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

m = (32 - 10)/(4 - 0)

m = 5.5

Now, the first coordinate has a y-intercept of 10. Thus, the equation here for the cost is; y = mx + c = 5.5x + 10

The slope of the second line is;

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

m = (15 - 0)/(2 - 0)

m = 7.5

Now, the first coordinate has a y-intercept of 0. Thus, the equation here for the cost is; y = mx + c = 7.5x + 0 = 7.5x

Thus, the system of equations representing these costs are;

y = 7.5x and y = 5.5x + 10

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Answer:

y = 7.5x and y = 5.5x + 10

Step-by-step explanation:

Answer:

40. 50c goes into 200 40 times

Answer:

the answer is 0.

Step-by-step explanation:

When you are adding two of the same numbers together, and one of them is positive while the other is negative, they cancel each other out.  

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathsf{-6 \dfrac{4}{5} + 6 \dfrac{4}{5}}[/tex]

[tex]\mathsf{= \dfrac{-6 \times 5 + 4}{5}+ \dfrac{6 \times 5 + 4}{5}}[/tex]

[tex]\mathsf{= \dfrac{-30 + 4}{5}+ \dfrac{30 + 4}{5}}[/tex]

[tex]\mathsf{= \dfrac{-34}{5} + \dfrac{34}{5}}[/tex]

[tex]\mathsf{= 0}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{0}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]