It's to the point that K Damon wants to make ice cream sundaes at this night's birthday party he thinks each person will eat 2 cups of ice cream and there will be 24 people is party a many one gallon tubs of ice cream should he left

Answer:

Grogg's dad is 22

Step-by-step explanation:

Let D = dad's current age

Let g = Grogg's current age

6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g

4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g

Set the two equations equal to each other and solve for d

6d - 35 = 4d - 9  Subtract 4d from both sides

2d -35 = -9  Add 35 to both sides

2d = 44  Divide both sides by 2

d = 22

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

d = current dad age

g = current grogg age

d-7 = 6(g-7)

d-3 = 4(g-3)

Let's solve the first equation first:

Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35

Substitude d = 6g - 35 for d in d - 3 = 4g - 12

(6g-35)-3 = 4g-12 = 6g-38 = 4g-12

Subtract 4g from both sides: 2g - 38 = -12

Add 38 to both sides: 2g = 26

Easy: g = 13

And now substitude g in for any equations.

d-3 = 52-12

d = 43

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

Answer:

7

Step-by-step explanation:

9 - 2 = 7

7 + 9 = 16

Mark as Brainliest

Answer:

\(a \sqrt[5]{b} \)

Step-by-step explanation:

solution Given:

\( \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } \)

since i indices rule if the power is same it can be multiplied or divided.

\( \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } \)

since power is added of like terms in multiplication

\( \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } \)

again simplifying

\( \sqrt[5]{ {a}^{5} b} \)

by using indices formula

\( \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } \)

we get

\(a \sqrt[5]{b} \)

Answer:

\(a \sqrt[5]{b}\)

Step-by-step explanation:

Given expression:

\(\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}\)

\(\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:\)

\((a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}\)

As the exponents are the same,

\(\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:\)

\((a^3b^2a^2b^{-1})^{\frac{1}{5}}\)

Collect like terms:

\((a^3a^2b^2b^{-1})^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\((a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}\)

Simplify the exponents:

\((a^5b^1)^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:\)

\((a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}\)

Simplify:

\(a^1 \cdot b^{\frac{1}{5}}\)

\(a \cdot b^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:\)

\(a \sqrt[5]{b}\)

Answer:

t = {4, 2}

Step-by-step explanation:

|3t-9| = 3

Split into two parts,

3t-9 = 3, and -(3t-9) = 3

Solve

t-3 = 1, and -(t-3) = 1

t = 4, and -t+3 = 1

t = 4, and t=2

At \($5 \mathrm{pm}$\) the distance between the ships is changing at the speed of \($\mathbf{3 0 . 2 1}$\) knots

Firstly we need to an equation to represent both ships and the distance between each. A is moving \($25 \mathrm{knots}$\) west and \($B$\) is moving \($17 \mathrm{knot}$\) north. \($D$\)will be the distance between the two. Drawing it, you'll notice that it creates a right triangle.

So we use the Pythagorean Theorem:

\($$D^{\wedge} 2=A^{\wedge} 2+B^{\wedge} 2$$\)

Differentiate in relation to time:

\($$2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt})$$\)

Now we must find all of our variables.

\(& A=\text { time(speed })+\text { original distance }=5(25)+10=135 \\\)

\(& B=5(17)+0=85 \\\)

\(& D=V\left(A^{\wedge} 2+B^{\wedge} 2\right)=159.53 \\\)

\(& d A / d t=25 \\\)

\(& d B / d t=17\)

Plug in all your variables and solve for

\($(\mathrm{dD} / \mathrm{dt})$ :\)

\(& 2 \mathrm{D}(\mathrm{dD} / \mathrm{dt})=2 \mathrm{~A}(\mathrm{dA} / \mathrm{dt})+2 \mathrm{~B}(\mathrm{~dB} / \mathrm{dt}) \\\)

\(& 2(159.53)(\mathrm{dD} / \mathrm{dt})=2(135)(25)+2(85)(17) \\\)

\(& 319.061(\mathrm{dD} / \mathrm{dt})=9640 \\\)

\(& \mathrm{dD} / \mathrm{dt}=9640 / 319.061 \\\)

\(& \mathrm{dD} / \mathrm{dt}=30.21 \text { knots }\end{aligned}\)

At \($5 \mathrm{pm}$\) the distance between the ships is changing at the speed of \($\mathbf{3 0 . 2 1}$\) knots

To know more about Pythagoras Theorem

https://brainly.com/question/343682

#SPJ4

Answer:

Step-by-step explanation:

You have two equations given and you want to solve all the couples (x; y) ∈ \(R^{2}\) that verifies both equations at the same time.

\(S:\left \{ {{2x-3y=5} \atop {-4x+5y=7}} \right.\)

First Method:

Substitution:

you need to give an expression of y in function of x or x in function of y in one of the two equations of the linear system, in order to replace the obtained expression in the other equation.

Example:

Take 2x-3y=5 <==> 2x = 5+3y <==> x = 5/2 + 3/2y

And now replace the obtained x in the other equation:

-4x + 5y = 7 <==> -4*(5/2+ 3/2*y) + 5y = 7 <==> -10 - 6y + 5y = 7

<==> -y = 17 <==> y = -17

and then you need to obtain x: 2x-3y=5

2x - 3*(-17) = 5 <==> 2x + 46= 0  <==> x = -23.

And the solutions are S = {(-23; -17)} ∈ \(R^{2}\)

Second Method:

Linear Combination:

You combine the two equations in order to have only one unknown value or variable an then you solve the set.

| 2x - 3y = 5                (*2)

| -4x + 5y = 7

| 4x -6y = 10

| -4x + 5y = 7

| 0 - y = 17 <==> y = -17

and then you need to obtain x: 2x-3y=5

2x - 3*(-17) = 5 <==> 2x + 46= 0  <==> x = -23.

So: S = {(-23; -17)} ∈ \(R^{2}\)

the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

To learn more on Compound interest click:

brainly.com/question/29335425

#SPJ1

Answer:

39.0625

Step-by-step explanation:

Answer:

39.0625

Step-by-step explanation:

Answer:

$104.90

Step-by-step explanation:

Did the math for you.

Have a good day!

Answer:

104.90 or 105$ rounded

Step-by-step explanation:

you do 20.98 (how much they cost) x 5 (how much he bought) = 104.90 (total cost.

Hope this helps :P

Answer:

(x-2)^2 + (y+3)^2 = 5.1^2

Step-by-step explanation:

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where h and k are the x and y values of the center of the circle respectively and r stands for the radius.

The center is given to us, at (2, -3) so we can plug that in:

(x-(2))^2 + (y- (-3))^2 = r^2

Simplify:

(x-2)^2 + (y+3)^2 = r^2

We can also solve for the radius by getting another point given to us: (3,2).

Using the pythagorean theorem, we can find how far the two points are away from each other:

a^2 + b^2 = c^2

1^2 + 5^2 = c^2
1 + 25 = c^2

26 = c^2

c ~ 5.1

Plug the radius we solved for in for r:
(x-2)^2 + (y+3)^2 = 5.1^2

Answer:

1). y= -4+ 4x

2). y= 3+ x/2

Step-by-step explanation:

hope this helps !

Answer:

1.56

Step-by-step explanation:

:)

Answer:

1.560

Step-by-step explanation:

3.9 x 0.4

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

For more such questions on original dimensions

https://brainly.com/question/31552973

#SPJ8

Answer:

2X+3+X-6 =180

3X-3+3=180+3

3X=183

X=61

Answer:

x = 61

Step-by-step explanation:

The angles shown form a straight line

Angles that form a straight line add up to equal 180

Hence, 2x + 3 + x - 6 = 180

( note that we just created an equation that we can use to solve for x )

We now solve for x using the equation created

2x + 3 + x - 6 = 180

step 1 combine like terms

2x + x = 3x

3 - 6 = - 3

we now have 3x - 3 = 180

step 2 add 3 to each side

-3 + 3 cancels out

180 + 3 = 183

we now have 3x = 183

step 3 divide 3 from each side

3x / 3 = x

183 / 3 = 6

we're left with x = 61

The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

We have to given that,

Functions are defined as,

⇒ s (x) = 2x²

⇒ f (x) = 3x

Now, We can find the value of (s - f) (- 7) is,

⇒ (s - f) (- 7)

⇒ s (- 7) - f (- 7)

⇒ 2 (- 7)² - (3 × - 7)

⇒ 2×49 + 21

⇒ 98 + 21

⇒ 119

Therefore, The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

Answer:

Please check if the answer is a = 4 or not

Answer:

1/2

Step-by-step explanation:

Let's consider the number we want is x

x-3/10=1/5

On both sides of the equation, if we substract (or add) a certain number, say 3/10, the equality relation still exists.

That is x-3/10+3/10=1/5+3/10

Then x=1/5+3/10

You see 1/5+3/10=2/10+3/10=1/2

So x=1/2

Answer:

I believe it is 200. Forgive me if its wrong-

Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:

p(x) = (x + 1) q(x)

for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:

p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0

So,

0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c

= -5 + 7 - 2 + 3 + c

= c = 3

So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.

What if the median is zero?

A variable that can in principle be only zero or positive can only have mean zero if all values in practice are zero. On the other hand, such a variable can and will have median zero if more than half of the values are zero.

Can you have a median of one number?

Median of one number = the number itself.

The key here is to not worry too much and just follow PEMDAS.

Here we have the expression \((5\cdot 7)^2\).  Following PEMDAS, we complete the expression inside the parentheses first, or \(5\cdot 7 = 35\). This gives us \((35)^2\) or just \(35^2.\)

Hope this helps.

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

⇒ -40 = 5x - x

⇒ 4x = -40

⇒ x = -40/4

⇒ x = -10

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

4x = -40

x = -10

There are 13 ways to make change for 60¢ using only nickels, dimes and quarters.

In the United States of America, a nickel equals 0.05 dollar, a dime equals 0.10 dollar and a quarter equals 0.25 dollar.  

For 0.60 dollar we have the following expression in terms of nickels (\(n\)), dimes (\(d\)) and quarters (\(q\)):

\(0.25\cdot q + 0.10\cdot d + 0.05\cdot n = 0.60\), where \(q,\,d,\,n \in \mathbb{N}_{O}\) (1)

Since quarters are the money of greatest value, we assume arbitrary quantities and count corresponding solutions, whose representations are included below:

\(n = 12-2\cdot d\) (2)

According to the first graph, there are seven forms in this scenario.

Case 2 (\(q = 1\))

\(n = 7-2\cdot d\) (3)

According to the graph case_2, there are four forms in this scenario.

\(n = 2- 2\cdot d\)

According to the graph case_3, there are two forms in this scenario.

Hence, there are 13 forms to make change for 60¢ using only nickels, dimes and quarters. \(\blacksquare\)

To learn more on combinations, we kindly invite to check this verified question: https://brainly.com/question/1216161

Answer:

m +m+m is equal to M3. hope it helps

Answer:

m.m.m

Step-by-step explanation:

I'm going to assume m3 signifies m³. If this be the case, then;

where as

but

The height of the building is approximately 227 feet.

In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.

The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.

As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.

Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF

On substituting the values from the given data, we get:

AE/(EF + 5.5) = 7/5.5.... (1)

Similarly, we can write from the given data:

BD/DF = 162/5.5.... (2)

From equations (1) and (2), we can write:

AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)

On solving the above equation for AE, we get:

AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft

Therefore, the height of the building is approximately 227 feet.

For more such questions on height, click on:

https://brainly.com/question/28122539

#SPJ8

Answer:

  $1025

Step-by-step explanation:

We can use the 2-point form of the equation of a line to write a function that gives Justin's salary as a function of his sales.

We start with (sales, salary) = (400, 500) and (700, 575)

__

The 2-point form of the equation of a line is ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  salary = (575 -500)/(700 -400)(sales -400) +500

  salary = 75/300(sales -400) +500

For sales of 2500, this will be ...

  salary = (1/4)(2500 -400) +500 = (2100/4) +500 = 1025

Justin's salary after selling $2500 in merchandise is $1025.

Answer:

The general plan is to find BM and from that CM. You need 2 equations to do that.

Step One

Set up the two equations.

(7 - BM)^2 + CM^2 = (4*sqrt(2) ) ^ 2 = 32

BM^2 + CM^2 = 5^2 = 25

Step Two

Subtract the two equations.

(7 - BM)^2 + CM^2  = 32

BM^2 + CM^2         = 25

(7 - BM)^2 - BM^2 = 7               (3)

Step three

Expand the left side of the new equation labeled (3)

49 - 14BM + BM^2 - BM^2 = 7    

Step 4

Simplify And Solve

49 - 14BM = 7              Subtract 49 from both sides.

-49 - 14BM = 7 - 49

- 14BM = - 42              Divide by - 14

BM = -42 / - 14

BM = 3

Step  Five

Find CM

CM^2 + BM^2 = 5^2

CM^2 + 3^2 = 5^2        Subtract 3^2 from both sides.

CM^2 = 25 - 9            

CM^2 = 16                     Take the square root of both sides.        

sqrt(CM^2) = sqrt(16)

CM = 4    < Answer

Step-by-step explanation: