At a bake sale, pies cost $8 each. One customer buys $64 worth of pies.

Answer:

a=2, b=3,x=6

Step-by-step explanation:

We are given that

We have to find the value of the missing letters in the sum of numbers.

From given sum

1+a+b=x   ....(1)

b+b+b=9  .....(2)

a+a=4       ......(3)

From equation (2) we get

[tex]3b=9[/tex]

[tex]\implies b=3[/tex]

From equation (3) we get

[tex]2a=4[/tex]

[tex]a=4/2[/tex]

[tex]a=2[/tex]

Now, substitute the values in equation (1) we get

[tex]1+2+3=x[/tex]

[tex]x=6[/tex]

Therefore,

231+32+233=496

Answer:

8ft

Step-by-step explanation:

We need to find out the length of the other leg of the triangle . Since it is a right angled triangle, we can use Pythagoras Theorem here , as,

[tex]\sf\implies h^2 = p^2 + b^2 \\\\\sf\implies (17ft)^2= p^2 + (15ft)^2\\\\\sf\implies 289 ft^2 - 225ft^2 = b^2 \\\\\sf\implies b^2 = 64 ft^2\\\\\sf\implies \underline{\underline{ base = 8 \ ft }}[/tex]

Answer:

C. 468 mm²

Step-by-step explanation:

Surface area of the composite solid = 2(LW + LH + WH)

Length (L) = 12 mm

Width (W) = 6 mm

Height (H) = 2 + 7 = 9 mm

Plug in the values into the formula

Surface area = 2(12*6 + 12*9 + 6*9)

Surface area = 2(72 + 108 + 54)

Surface area = 2(234)

= 468 mm²

Answer:

You could save $20

Step-by-step explanation:

For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130

Answer:

20 dollars

Step-by-step explanation:

for the first deal is 5 for $130

and the second is for $30

$30 times 5 (the number of people) = $150

$150-$130= is 20

answer: $20

Answer:

45

Step-by-step explanation:

Answer:

[tex]44[/tex]

Step-by-step explanation:

The dimensions of the garden is 12 by 8. If we have a walkway that surrounds the garden, the dimensions of the walkway is 2. Since it surrounds the rectangle all sides add 2 to each of the dimensions so now the dimensions of the garden and walkway is 14×10.

The area of the garden is 96 square ft.

The area of the garden and walkway is 140 so let subtract the area of the garden from the total area of both the garden and walkway.

[tex]140 - 96 = 44[/tex]

The area is 44.

Answer:

120 square feet

Step-by-step explanation:

(8+2*2)

(18+2*2) - 8*18 = 120 square feet.

Answer:

1) 6m+8n

4) 21x+14y

7) 14c+16d

10) d+3e

Step-by-step explanation:

Step 1: Distribute

-40a - 5 + 6 = 281

Step 2: Combine Like Terms

-40a + 1 = 281

Step 3: Move Variables and Constants to Different Sides

-40a = 280

Step 4: Divide

a = -7

Hope this helps!

a = -7

-5 ( 8a + 1 ) + 6 = 281

Step 1 :- Distribute -5 through parantheses.

Step 2 :- Combine like terms.

Step 3 :- Move constant to right-hand side and change their sign.

Step 4 :- Subtract the numbers.

Step 5 :- Divie both side by -40 .

Hello,

P(A)=0.4

P(B)=0.3

P(AUB)+P(A∩B)=P(A)+P(B)

P(AUB)=0.4+0.3-0.1=0.6

Answer C

The correct answer is option (C).

P(A ∪ B) = 0.6

If A, B are two different events then P(A U B) = P(A) + P(B) - P(A ∩ B)

We have been given, P(A) = 0.4, P(B) = 0.3

From given Venn diagram,

P(A ∩ B) = 0.10

Now, P(A U B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A U B) = 0.4 + 0.3 - 0.10

⇒ P(A ∪ B) = 0.6

Therefore, the correct answer is option (C) .6

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Answer:

The difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.

Step-by-step explanation:

The pH is given by:

[tex] pH = -log[H^{+}] [/tex]

Where:

[tex] [H^{+}][/tex]: is the concentration of hydrogen ions.

For the basic solution (pH = 11.2), the concentration of H⁺ is given by:

[tex] [H^{+}]_{b} = 10^{-pH} = 10^{-11.2} = 6.31 \cdot 10^{-12} [/tex]

And, for the acidic solution (pH = 2.4) we have:

[tex] [H^{+}]_{a} = 10^{-pH} = 10^{-2.4} = 3.98 \cdot 10^{-3} [/tex]

Hence, the difference in the concentration of H⁺ between the two solutions is:

[tex] \Delta H^{+} = [H^{+}]_{a} - [H^{+}]_{b} = 3.98 \cdot 10^{-3} - 6.31\cdot 10^{-12} = 3.98 \cdot 10^{-3} [/tex]

Therefore, the difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.

I hope it helps you!

Answer:

B. 4.0 x [tex]10^{-3}[/tex]

Step-by-step explanation:

EDG2021

Answer:

FALSE

Step-by-step explanation:

The regression equation is a prediction model which is generated for a given independent, x and dependent, y variable. The regression model is usually ideal when both the dependent and independent variables are numerical. The regression equation cannot be generated if either the x or y value is non-numeric. In such situation, classification models may be better suited for such cases especially if there is no efficient method of converting the non-numeric column into a numeric variable.

A parallelogram is also a rhombus if the diagonal is a bisector of an angle enclosed by the two adjacent sides of a parallelogram.

In our case it means,

[tex]5x+25=12x+11[/tex]

[tex]7x=14\implies x=\boxed{2}[/tex]

Hope this helps.

In order for the parallelogram to be a rhombus, ,For the parallelogram to be a rhombus, x must be equal to 2.

To determine the value of x that would make the parallelogram a rhombus, we need to compare the lengths of its opposite sides. In a rhombus, all four sides are equal in length. So, we can equate the lengths of the opposite sides of the parallelogram and solve for x.

Given that one side has a length of (5x + 25) and the opposite side has a length of (12x + 11), we can set up the following equation: 5x + 25 = 12x + 11

To solve for x, we can start by isolating the x term on one side of the equation. We can do this by subtracting 5x from both sides: 25 = 12x - 5x + 11 Simplifying the equation further: 25 = 7x + 11 Next, we can isolate the x term by subtracting 11 from both sides: 25 - 11 = 7x 14 = 7x Finally, we can solve for x by dividing both sides by 7: 14/7 = x x = 2 Therefore, for the parallelogram to be a rhombus, x must be equal to 2.

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Answer:

D

Step-by-step explanation:

Slope of the first line = (1-3)/1 = -2

Answer:

volume =l×b×h

45cm×32cm×35cm=48,960cm³

Answer:

y = 480 + 1.5 (x-40)

Step-by-step explanation:

sometimes its better to answer the question and make the formula from that

40 x 12 = 480

1.5 for overtime

x

y = 480 + 1.5 (x-40)

Answer:

Use calculation for the population  standard deviation

Step-by-step explanation:

We are given that the data data set represents the ages of all 6 of Nancy's grandchildren

11,8,5,6,3,9

We have to determine which standard deviation would used for calculation of  the given data set.

Sample standard deviation :If the data values represent the data collected from   subset of  population .Then the sample standard deviation should be used.

Population standard deviation:

If the data values represents the data collected from entire population, then population standard deviation should be used.

We can see that the given data collected from entire population.

Therefore, we would use  calculation for population standard deviation of given data set.

Answer:

LP ⊥ PN

Step-by-step explanation:

Given

[tex]L = (-4, 1)[/tex]

[tex]M = (2, 4)[/tex]

[tex]N = (3, 2)[/tex]

[tex]P = (-3, -1)[/tex]

See attachment

Required

What proves LMNP is a rectangle

The additional information needed is LP ⊥ PN

Because:

[tex](a)\ LM= \sqrt{45}; MN = \sqrt{5}[/tex]

This can be true for other shapes, such as trapezoid, etc.

[tex](b)\ m(LP) = m(MN) = -2[/tex]

The slopes of LP and MN will be the same because both sides are parallel; However, this is not peculiar to rectangles alone. Same as option (c)

(d) LP ⊥ PN

This must be true i.e. LP must be perpendicular to PN

Answer:

d

Step-by-step explanation:

Answer:

0.7513 = 75.13% probability that no more than 1 employee was over 50

Step-by-step explanation:

The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4 + 16 = 20 employees, which means that [tex]N = 20[/tex]

4 over 50, which means that [tex]k = 4[/tex]

5 were dismissed, which means that [tex]n = 5[/tex]

What is the probability that no more than 1 employee was over 50?

Probability of at most one over 50, which is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]

[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]

0.7513 = 75.13% probability that no more than 1 employee was over 50

Answer:

f(x) = 8x

Explanation:

4 x 2 =8

HCF=15

Hope it helps you...

Answer:

11 + 10i

Step-by-step explanation:

Just treat i like any other variable, and combine like terms. Hope that helps!

Answer:

x = 3.5

Step-by-step explanation:

Triangle to the right:

4^2 + x^2 = 8^2

16 + x^2 = 64

y^2 = 48

Triangle to the left:

x^2 + 6^2 = 48

x^2 + 36 = 48

x^2 = 12

x = sqrt(12)

x = 3.5

Answer:

7 digits can be used for each position

There are a total of 5 positions

N = 7^5 = 16,807 numbers

You have 7 choices for the first position, second position, etc.

Answer:

a) Minimize Z =30 X1 +25 X2+18 X3

subject to following constraints

[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]

b) Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.

c) As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.

Step-by-step explanation:  

Step 1:-

a)  

Let's take  

X1 to be the number of hours assigned to Lisa  

X2 to be the number of hours assigned to David  

X3 to be the number of hours assigned to Sarah.  

The objective function is to attenuate the entire cost of the project by deciding an optimum number of hours for every person. the target function is given by -  

Minimize Z =30 X1 +25 X2+18 X3

subject to following constraints

[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]  

Constraints and explanation:  

1. Lisa must be assigned a minimum of 40% of the entire number of hours assigned to the 2 senior designers.  

2. Sarah must be assigned a minimum of 15% of the entire project time.  

3. The corporate estimates that 150 hours are going to be required to finish the project.  

4. The number of hours assigned to Sarah must not exceed 25% of the entire number of hours assigned to the 2 senior designers.  

5. Lisa features a maximum of fifty hours available to figure on this project.  

6. Non-negative condition.  

Step 2:-  

b)

From the above equations, we get  

The number of hours assigned to Lisa is 48 hours  

The number of hours assigned to David 72 hours  

The number of hours assigned to Sarah 30 hours.  

Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.  

Step 3:-

c)  

As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.

Answer:

-15.875

Step-by-step explanation:

First, we can sum up the first 5 terms.

-8 + (-4) = -12

-12 + (-2) = -14

-14 + (-1) = -15

-15 + (-1/2) = -15.5

Next, we can find a pattern in the data. We can tell that the next number is one half of the current number. For example, -4 is one half of -8. To find the next number, we simply multiply our current number by one half. Thus, the sixth number is -1/4 and the seventh is -1/8. Adding these to our current total, we have

-15.5 - 1/4 = -15.75

-15.5 - 1/8 = -15.875 as our answer

Answer:

20

Step-by-step explanation:

a)x^2+16^2=a^2

b)x^2+25^2=b^2

c)a^2+b^2=(16+25)^2

a+b)2x^2+25^2+16^2=41^2=a^2+b^2

2x^2=800

x=20

Answer:

[tex]y=\frac{1}{2}x+5[/tex]

Step-by-step explanation:

Hi there!

Slope intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two points that lie on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug the given points (-4,3) and (6,8) into the equation

[tex]m=\frac{8-3}{6-(-4)}\\m=\frac{8-3}{6+4}\\m=\frac{5}{10}\\m=\frac{1}{2}[/tex]

Therefore, the slope of the line is [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex] :

[tex]y=\frac{1}{2}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{2}x+b[/tex]

Plug in one of the given points and solve for b

[tex]8=\frac{1}{2}(6)+b\\8=3+b[/tex]

Subtract 3 from both sides to isolate b

[tex]8-3=3+b-3\\5=b[/tex]

Therefore, the y-intercept is 5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:

[tex]y=\frac{1}{2}x+5[/tex]

I hope this helps!

Answer:

3.82

Step-by-step explanation:

[tex]\sqrt{(9+\sqrt{32}) }[/tex] Do not confirm the answer unless your equation looks like that?

[tex]\sqrt{(9+\sqrt{32}) }[/tex] Start by the [tex]\sqrt{32}[/tex]

[tex]\sqrt{(9+5.65) }[/tex] Now add (9 + 5.65)

[tex]\sqrt{14.65}[/tex]         Finally Simplify

[tex]3.82[/tex]              Final answer

Answer:

2/7 = 4/14 so from smallest to largest the fractions are:

2/7 4/14 and 8/11

Step-by-step explanation:

Answer:

125x=(62.50+(62.50)×0