Alex and Amber are both saving money for a
summer vacation. Alex has already saved $100 and
plans to save $25 per week until the trip. Amber has
$75 and plans to save $30 per week. In how many
weeks will Alex and Amber have the same amount of
money?
19 points!

Answer: 4, 800

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

The concentration of a drug in an organ at any time t (in seconds) is given by s 0.25t - 15(1 - e-t/60) if osts 20 | 15e-t/60 – 10e-(t - 20)/60 if t> 20 where c(t) is measured in milligrams per cubic centimeter (mg/cm3). (a) What is the initial concentration of the drug in the organ? 0 mg/cm3 (b) What is the concentration of the drug in the organ after 14 sec? (Round your answer to three decimal places.) x mg/cm3 38 (c) What is the concentration of the drug in the organ after 40 sec? (Round your answer to three decimal places.) mg/cm3 Need Help? | Read It

After value putting, if the number of guests represented by the variable (g) is 17 then the cost pf the food is $220.

In the given question we have to evaluate the expression if the number of guests represented by the variable (g) is 17.

An expression to represent the cost of the food for a catered lunch is 50+10g.

The fee for the catering is $50 and then there is a $10 charge for each lunch box.

Since g is representing the number of guests.

The the value of g is given 17.

Now putting the value of g in the given expression.

=50+10g

=50+10*17

=50+170

=220

Hence, if the number of guests represented by the variable (g) is 17 then the cost pf the food is $220.

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Answer:

1.42217 or 1.42

Step-by-step explanation:

Using the formula

V=whl

Solving for L

L=V/HW=150.75/8x13.25≈1.42217

Answer:

10

Step-by-step explanation:

f(x)=3x-1

g(x)= - 2x-4.  

g( f(-2))

First find f(-2)

Let x = -2

f(-2)=3(-2)-1 = -6-1 = -7

Now find g(-7)

g(-7) = -2(-7) -4 = 14 -4 = 10

Answer:

\(f(x) = 3x - 1 \\ g(x) = - 2x - 4 \\ g(f(x)) = - 2(3x - 1) - 4 \\ g(f(x)) = - 6x + 2 - 4 \\ g(f(x)) = - 6x - 2 \\ g(f( - 2)) = - 6( - 2) - 2 \\ g(f( - 2)) = 12 - 2 \\ \boxed{g(f( - 2)) = 10}\)

Answer:

1.2 pounds of chicken per serving.

Step-by-step explanation:

4 and 4/5 of pounds of chicken for serving of 4.

We can also write this as 4.8 pounds of chicken.

To find how much pound of chicken will be needed for a single serving we have to divide 4.8 by 4.

\( \frac{4.8}{4} = 1.2 \: pounds \: of \: chicken\)

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Thanks!

Answer:

A)     (0, -1)

Step-by-step explanation:

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph)

(0, -1)

Answer:

Step-by-step explanation:

\(\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+2} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\stackrel{\textit{one intercept}}{\textit{\underline{one solution}}}\qquad \\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ 4^2-4(2)(2)\implies 16-16\implies 0\)

Answer:

3.33

4.33

TVE figures is that

Answer:

B 180

Step-by-step explanation:

The period is the interval it takes to repeat

The bottom of the first curve to where it repeats is 180

Answer:

5.44

Step-by-step explanation:

1.6*3.4=5.44

9514 1404 393

Answer:

  24

Step-by-step explanation:

Find the parts of the expression from the graph, and evaluate the expression.

  f(6) = -6

  g(5) = -5

Then we have ...

  f(6) -6·g(5) = (-6) -6(-5) = -6 +30 = 24

The value of y when a = 1 and b = 2 is 22.

The equation of can be solved as follows: We will substitute the value of a and b  in the equation to find the value of y.

Therefore,

y = 3ab + 2b³

Let's find y when a = 1 and b = 2

Hence,

y = 3(1)(2) + 2(2)³

y = 6 + 2(8)

y = 22

Therefore,

y = 22

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Answer:

y = x - 5

Step-by-step explanation:

Comparing the given y = x - 7 to y = mx + b, we see that the slope is +1.

In y = x + b we replace y with -11 and x with -6 to determine the y-intercept, b:

-11 = -6  + b

Then b must be -5, and so the desired new equation is

y = x - 5

Answer:

The orthocentre of the given vertices ( 2 , -3.5)

Step-by-step explanation:

Step(i):-

The orthocentre is the intersecting point for all the altitudes of the triangle.

The point where the altitudes of a triangle meet is known as the orthocentre.

Given Points are K (3.-3), L (2,1), M (4,-3)

The Altitudes are perpendicular line from one side of the triangle to the opposite vertex

The altitudes are  MN , KO , LP

step(ii):-

   Slope of the line  

                          \(KL = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{1-(-3)}{2-3} = -4\)

The slope of MN =

The perpendicular slope of KL

                           = \(\frac{-1}{m} = \frac{-1}{-4} = \frac{1}{4}\)

The equation of the altitude

                                 \(y - y_{1} = m( x-x_{1} )\)

                                \(y - (-3) = \frac{1}{4} ( x-4 )\)

                               4y +12 = x -4

                                x - 4 y -16 = 0 ...(i)

Step(iii):-

 Slope of the line  

                          \(LM = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{-3-1}{4-2} = -2\)

The slope of KO =

The perpendicular slope of LM

                           = \(\frac{-1}{m} = \frac{-1}{-2} = \frac{1}{2}\)

The equation of the altitude

                                 \(y - y_{1} = m( x-x_{1} )\)

The equation of the line passing through the point K ( 3,-3) and slope

m = 1/2

                                \(y - (-3) = \frac{1}{2} ( x-3 )\)

                                2y +6 = x -3

                             x - 2y -9 =0 ....(ii)    

Solving equation (i) and (ii) , we get

  subtracting equation (i) and (ii) , we get

                   x - 4y -16 -( x-2y-9) =0

                       - 2y -7 =0

                      -2y = 7

                        y = - 3.5

Substitute y = -3.5 in equation x -4y-16=0

               x - 4( -3.5) - 16 =0

               x +14-16 =0

                x -2 =0

                  x = 2

The orthocentre of the given vertices ( 2 , -3.5)

The length of the guy wire, to the nearest foot is 48 ft.

A unit of length (or distance) in US units equal to 12 inches. The abbreviation is: ft. Or sometimes the single quote mark: ' Example: 10 feet can be written 10 ft, or just 10' A foot is exactly 0.3048 meters in the Metric System (the foot is defined that way).

Step-by-step explanation:

Here, we want to find the length of the wire

from the diagram, we can identify two similar triangles

The smaller one and a bigger one

Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal

We can start by getting the height of the tower

we have this as:

8/11 = 28/x

8 * x = 28 * 11

8x = 308

x = 308/8

x = 38.5 ft

So as we can see, the wire represents the hypotenuse of the larger triangle that measures 28 ft base and 38.5 ft height

So we can use the Pythagoras’ theorem to get the hypotenuse

Let us call this g mathematically;

According to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

thus, we have it that;

g^2 = 38.5^2 + 28^2

g^2 = 2,266.25

g = √2,266.25

g = 47.61 which is approximately 48 ft

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Answer:

Part 1

Part 2

Part 3

Answer:

\(S = \{A, B, AB, O\}\)

Step-by-step explanation:

Given

Blood groups: A, B, AB and O

\(n = 1500\)

\(A = 438\)

\(B = 350\)

\(AB = 95\)

\(O = 617\)

Required

The sample space for blood type

To determine the sample space, we will consider the blood groups being sampled

So, the sample space is:

\(S = \{A, B, AB, O\}\)

And the sample size is:

\(Size = n(S)\)

\(Size = 4\)

Step-by-step explanation:

Blood groups: A, B, AB and O

n = 1500n=1500

A = 438A=438

B = 350B=350

AB = 95AB=95

O = 617O=617

Required

The sample space for blood type

To determine the sample space, we will consider the blood groups being sampled

So, the sample space is:

S = \{A, B, AB, O\}S={A,B,AB,O}

And the sample size is:

Size = n(S)Size=n(S)

Size = 4Size=4

9514 1404 393

Answer:

Step-by-step explanation:

1) Divide both sides by the coefficient of x.

  x = (7.2/(-14/9))/((-108/35)/(-2/3))

  x = -1

__

2) Multiply both sides by the factor x is being divided by.

  x = (-3.18/5.3)/((-20/3)/(-2))

  x = -2

_____

Your calculator can help you with this.

Answer:

The circumference of a circle is the distance around the entire circle, while arc length, s, is the distance between two points on the circle.

C = 2πr = 2π( 5 ) = 10π ≈ 31.4 units

3.14 is an approximation for π.

s = θ/360° (C)

mAB = 60°/360° ( 31.4)

= 1/6(31.4) ≈5.2 units

The available options are

A) 10

B) 11

C) 30

D) 91

E) The number depends on the size of the population.

Answer:

91

Step-by-step explanation:

Given that for the normal approximation, we need that:

np > 5 and np(1-p) > 5

Hence, we have

n = 91

91*0.89 = 80.99

91*0.89*0.11 = 8.9089 > 5

Therefore the answer gotten is satisfactory or satisfies the condition, and which makes 91 the accurate solution.

The other options, when calculated is less than 5

Let's write this verbal phrase as an inequality.

First of all, let the number be n.

"three times n" can be written like so:-

\(\pmb{3n}\)

Now, 18 is greater than 3n:-

\(\pmb{18 > 3n}\)

Which means 3n is less than 18:-

\(\bigstar{\boxed{\pmb{3n < 18}}}\)

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)