Let f (x )equals x squared and note that Modifying Below lim With x right arrow 2​f(x)equals 4. For epsilon equals 1​, use a graphing utility to find the maximum value of delta greater than 0 such that StartAbsoluteValue f (x )minus 4 EndAbsoluteValue less than epsilon whenever 0 less than StartAbsoluteValue x minus 2 EndAbsoluteValue less than delta.

Answer: she invested $17000 in the account earning 6% annual interest.

she invested $13000 in the account earning 7.5% annual interest.

Step-by-step explanation:

Let x represent the amount that she invested in the account earning 6% annual interest.

Let y represent the amount that she invested in the account earning 7.5% annual interest.

Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. This means that

x + y = 30000

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the account earning 6% annual interest.

P = x

R = 6%

T = 1 year

I = (x × 6 × 1)/100 = 0.06x

Considering the account earning 7.5% annual interest,

P = y

R = 7.5

T = 1

I = (y × 7.5 × 1)/100 = 0.075y

Last year she earned $1995 in interest. This means that

0.06x + 0.075y = 1995 - - - - - - - -

Substituting x = 30000 - y into equation 1, it becomes

0.06(30000 - y) + 0.075y = 1995

1800 - 0.06y + 0.075y = 1995

- 0.06y + 0.075y = 1995 - 1800

0.015y = 195

y = 195/0.015 = 13000

x = 30000 - y = 30000 - 13000

x = 17000

Answer:

  3

Step-by-step explanation:

Each term of the sequence has 0.5 added to the one before. The first 10 terms are ...

  -1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0

f(10) = 3.0

_____

If you like, you can use the given information about the first term (-1.5) and the common difference (0.5) to write an explicit formula:

  f(n) = f(1) +d(n -1)

  f(n) = -1.5 +0.5(n -1)

Then the 10th term is ...

  f(10) = -1.5 +0.5(10 -1) = -1.5 +4.5 = 3

Henry will have run a total of 1540 miles on his new running shoes after 5 weeks.

To find the total mileage on Henry's shoes after 5 weeks, we need to calculate the distance he runs each week and add them up.

In week 1, Henry runs 20 miles per day, so the total distance he runs in week 1 is 20 miles * 7 days = 140 miles.

In week 2, he adds 12 miles to his daily routine, so he runs 20 miles + 12 miles = 32 miles per day. The total distance he runs in week 2 is 32 miles * 7 days = 224 miles.

We can continue this pattern for the remaining weeks:

Week 3: 44 miles per day, total distance = 44 miles * 7 days = 308 miles

Week 4: 56 miles per day, total distance = 56 miles * 7 days = 392 miles

Week 5: 68 miles per day, total distance = 68 miles * 7 days = 476 miles

The total mileage on Henry's shoes after 5 weeks is the sum of the total distances in each week: 140 + 224 + 308 + 392 + 476 = 1540 miles.

The probability of having wrinkled green peas is 25% or 0.25

Explanation:

Given:

Pea shape - smooth and wrinkled

Pea color - Yellow and green

Smooth is dominant to wrinkled

Yellow color is dominant to green

So, the genotype of smooth pea is SS or Ss

                                 wrinkled pea is ss

The genotype of yellow pea is YY or Yy

                                 green pea is yy

According to the question,

Ssyy X ssYy

Possible gametes of Ssyy - Sy , Sy, sy, sy

Possible gametes of ssYy - sY, sy, sY, sy

Cross between these gametes are shown in the punnett square drawn in the word file attached.

According to the cross,

The probability of having wrinkled green peas is 25% or 0.25

Answer:

(A)  [tex]C(x)=2.15x+525[/tex]

(B) 188 books

(C) 545 books

Step-by-step explanation:

We have been given that Alfred Juarez's fixed cost to produce a typical poetry volume is $525, and his total cost to produce 1000 copies of the book is $2675.

(A) The cost function will be in form [tex]C(x)=ax+b[/tex], where, a is cost of each copy, x is number of books and b is fixed cost.

Upon substituting our given information, we will get:

[tex]2675=1000a+525[/tex]

Let us solve for a.

[tex]2675-525=1000a[/tex]

[tex]2150=1000a[/tex]

[tex]a=\frac{2150}{1000}=2.15[/tex]

Therefore, the cost function would be [tex]C(x)=2.15x+525[/tex].

(B) Since each book sells for $4.95, so amount earned by selling x books would be [tex]4.95x[/tex]

Revenue function would be [tex]R(x)=4.95x[/tex]

We know that break-even is a point, where cost is equal to revenue or when there is a 0 profit.

[tex]R(x)=C(x)\\\\4.95x=2.15x+525[/tex]

[tex]4.95x-2.15x=525[/tex]

[tex]2.8x=525[/tex]

[tex]x=\frac{525}{2.8}[/tex]

[tex]x=187.5\approx 188[/tex]

Therefore, Alfred must produce 188 poetry books to break even.

(C) We know that profit is equal to difference of revenue and cost.

[tex]\text{Profit}=\text{Revenue}-\text{Cost}[/tex]

[tex]P(x)=4.95x-(2.15x+525)[/tex]

[tex]1000=4.95x-(2.15x+525)[/tex]

[tex]1000=4.95x-2.15x-525[/tex]

[tex]1000=2.8x-525[/tex]

[tex]1000+525=2.8x[/tex]

[tex]1525=2.8x[/tex]

[tex]x=\frac{1525}{2.8}[/tex]

[tex]x=544.642857\approx 545[/tex]

Therefore, Alfred must produce and sell 545 books to make a profit of $1000.

Step-by-step explanation:

∫₋₂² (f(x) + 6) dx

Split the integral:

∫₋₂² f(x) dx + ∫₋₂² 6 dx

Graphically, if f(-x) = -f(x), then ∫₋₂² f(x) dx = 0.  But we can also show this algebraically.

Split the first integral:

∫₋₂⁰ f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Using substitution, write the first integral in terms of -x.

∫₂⁰ f(-x) d(-x) + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₂⁰ f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Flip the limits and multiply by -1.

∫₀² f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Rewrite f(-x) as -f(x).

∫₀² -f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₀² f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

The integrals cancel out:

∫₋₂² 6 dx

Evaluating:

6x |₋₂²

6 (2 − (-2))

24

Answer:

Therefore the value of x is

[tex]x=5[/tex]

Step-by-step explanation:

Given:

Consider the figure such that

PQ || BC

AP = 20 , AB = 36

AQ = 5x , AC = 45

To Find:

x = ?

Solution:

In Δ APQ and Δ ABC

∠APQ ≅ ∠ACB {Corresponding angles are equal since PQ is parallel to BC}

∠A≅ ∠A  ……….....{Reflexive Property}  

Δ APQ~ Δ ABC….{Angle-Angle Similarity test}  

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}=\dfrac{PQ}{BC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}\\\\\dfrac{20}{36} =\dfrac{5x}{45}\\\\x=\dfrac{20\times 45}{36\times 5}=5\\\\x=5[/tex]

Therefore the value of x is

[tex]x=5[/tex]

Answer:

3 gallons

Step-by-step explanation:

If two gallons of paint covers 800 square feet, 'x' gallons of paints will cover 1200square feet room where x is the number of gallons needed to paint the 1200 square feet room.

Mathematically,

2 gallons = 800sq.ft

x gallons = 1,200sq.ft

x × 800 = 2 × 1200

x = 2 × 1200/800

x = 3 gallons

Therefore Leah will need 3gallons of paint for 1200sq.ft room

Answer:

Some details are missing in the question, here are the details ; A proton initially has v = -6.5i + 17j + 13k and then 8.00s later has v = -2.8i + 17j - 9.3k (in meters per seconds).

a) proton's average acceleration in unit vector notation = 0.46i - 2.78k

b) Magnitude = 2.85m/s2

c) angle between and the positive direction of the x axis = 279.39 degree (counter clockwise)

Step-by-step explanation:

The detailed and step by step explanation is as shown in the attachment

Answer:

[tex]m\angle E=58^o[/tex]

Step-by-step explanation:

we know that

In the right triangle DEF

[tex]tan(E)=\frac{DF}{EF}[/tex] ----> by TOA (opposite side divided by adjacent side)

[tex]tan(E)=\frac{8}{5}[/tex]

[tex]m\angle E=tan^{-1}(\frac{8}{5})=58^o[/tex]

Answer:

Exact circumference is [tex]7\frac{49}{150}km[/tex]

Approximate circumference is [tex]7.33 km[/tex]

Step-by-step explanation:

We are given;

We are required to determine the exact and approximate circumference of the circle.

Taking π as 3.14

[tex]Circumference=3.14 (2\frac{1}{3}km)[/tex]

                          [tex]=7\frac{49}{150}km[/tex]

The exact circumference of the circle is [tex]7\frac{49}{150}km[/tex]

[tex]7\frac{49}{150}km=7.327 km\\ = 7.33 km (nearest hundredth)[/tex]

Thus, the approximate circumference of the circle is [tex]7.33 km[/tex]

Answer:

a.)   depth of the lake = (volume of the lake) / area of lake

            = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet

b.) 11 inches  = 0.9167 feet

    Water gained in cubic feet gained by the lake

         = 624,305,840,400 [tex]\times[/tex]  0.9167  

         = 572,282,434,719.5 cubic feet

c.) the percentage change in the lake volume over that year

      = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet

      =  0.0033

      = 0.33%

Step-by-step explanation:

i) acres to square feet :    1 acre = 43560 square feet

  therefore 14,332,090 acres  = 624,305,840,400 square feet

ii) 1 mile  = 5280 feet

   1 cubic mile  = 5280 [tex]\times[/tex] 5280 [tex]\times[/tex] 5280 = 147,197,952,000 cubic feet

therefore 1180 cubic miles  = 173,693,585,360,000 cubic feet

a.)   depth of the lake = (volume of the lake) / area of lake

            = 173,693,585,360,000 / 624,305,840,400  = 278.22 feet

b.) 11 inches  = 0.9167 feet

    Water gained in cubic feet gained by the lake

    = 624,305,840,400 [tex]\times[/tex]  0.9167   = 572,282,434,719.5 cubic feet

c.) the percentage change in the lake volume over that year

  = 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet

   =  0.0033

  = 0.33%

Answer:

5 km walking, 30 km on the bus.

Step-by-step explanation:

Let

w

be the distance walking and

b

be the distance on the bus.

The total distance is 35 km.

w

+

b

=

35

The total time is 1.5 hours. Each leg has time equal to distance/speed.

w

5

+

b

60

=

1.5

Multiply by 60 to clear the fractions.

12

w

+

b

=

90

Subtract the first equation,

11

w

=

90

−

35

=

55

w

=

5

b

=

30

Check:

Answer:

7

Step-by-step explanation:

[tex]\sum\limits_{t=1}^{3}(4\cdot(\frac{1}{2})^{t-1})[/tex]

This is the sum of the first three terms of a geometric sequence, where the first term is 4 and the common ratio is ½.

We can use a formula to find the sum, or, since there's only three terms, we can find the value of each term then add up the results.

4 · (½)¹⁻¹ = 4

4 · (½)²⁻¹ = 2

4 · (½)³⁻¹ = 1

4 + 2 + 1 = 7

Mean and Mean Absolute Deviation

Step-by-step explanation:

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Here's how to calculate the mean absolute deviation.

Step 1: Calculate the mean.

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

Step 3: Add those deviations together.

Step 4: Divide the sum by the number of data points.

Answer:

Rocket will land on the ground in 3 seconds.

Step-by-step explanation:

Given:

[tex]A(t) = -16t^2 + 32t + 48[/tex]

where [tex]t[/tex] ⇒ time in seconds since launch.

[tex]A(t)[/tex] ⇒ altitude of the rocket after reaching the ground.

we need to find the time at which rocket will land on the ground.

Solution:

Now we can say that;

altitude of the rocket after reaching the ground will be equal to 0.

So;

[tex]A(t)=0[/tex]

Now Substituting [tex]A(t)=0[/tex] in given expression we get;

[tex]0=-16t^2+32+48[/tex]

Now we take -16 common we get;

[tex]0=-16(t^2-2t-3)[/tex]

Now Dividing both side by -16 we get;

[tex]\frac0{-16}=\frac{-16(t^2-2t-3)}{-16}\\\\0=t^2-2t-3[/tex]

Now factorizing the above equation we get;

[tex]0=t^2-3t+t-3\\\\0=t(t-3)+1(t-3)\\\\0=(t+1)(t-3)[/tex]

Now we will find 2 values of t by substituting each separately.

[tex]t+1=0 \ \ \ Or \ \ \ \ t-3 =0\\\\t =-1 \ \ \ \ \ \ Or \ \ \ \ \ \ t=3[/tex]

Now we get 2 values of t one positive and one negative.

Now we know that time cannot e negative hence we will discard it and consider positive value of t.

Hence Rocket will land on the ground in 3 seconds.

Answer:3.46$

Step-by-step explanation:

Probability distribution:

[tex]\to x \ \ \ \ \ \ \ -\$5 \ \ \ \ \ \ \ \$0 \ \ \ \ \ \ \ \$5\\\\\to P(x) \ \ \ \ \ \ \ 0.36 \ \ \ \ \ \ \ 0.48 \ \ \ \ \ \ \ 0.16\\\\[/tex]

[tex]\to \mu_{x}= Mean\ (X)= E(X) \ = - \$ 1\\\\\to \sigma^{2}_{x}= \Sigma_{x} x^2 p(x)- (\mu_{x})^2\\\\[/tex]  

         [tex]=(-5)^2 \times 0.36 + 0+ (5)^2 \times 0.16 - (-1)^2\\\\=25 \times 0.36 + 0+ 25 \times 0.16 - 1\\\\=9 + 0+ 4 - 1\\\\= 13-1\\\\=12\\\\[/tex]

Therefore,  

[tex]\to \sigma_{x}=\sqrt{12}= \$ 3.464[/tex]

Therefore, the final answer is "3.464".

Learn more about the probability distribution:

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Answer: The number of revolutions the tire makes per minute= 840.76

Step-by-step explanation:

Given : Diameter of tire = 24 inches

Speed of car = 60 mi/ hr

We know that 1 mile =63360 inches and 1 hour = 60 minutes

Then, Speed of car =  ( 60 mi/ hr) x( 63360 inches) ÷ (60 minutes)

[tex]=\dfrac{60\times63360 }{60}[/tex]  inches/minute

=63360 inches / minute

Circumference of tire = [tex]\pi (diameter)[/tex]

[tex](3.14)(24)=75.36\ inches[/tex]

Now , the number of revolutions the tire makes per minute = [tex]\dfrac{\text{speed of car}}{\text{Circumference of tire}}[/tex]

[tex]=\dfrac{63360}{75.36}=840.76433121\approx840.76[/tex]

Hence, the number of revolutions the tire makes per minute= 840.76

Answer:

subtract 27 from 85

Step-by-step explanation:

85

-27

———

58

7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracted from 15 and then the 8 tens becomes 7 tens so 7-2=5

58+27=85 to check your work

We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

Given that regroup 1 ten as 10 one

85 -27 = 58

Since 7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracbecomem 15 and then the 8 tens becomes 7 tens thus, 7-2=5

Therefore,

58 + 27 = 85

We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85

Learn more about a number pattern:

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Answer:

52.2

Step-by-step explanation:

Light reflects off a mirror at the same angle it hits it at (as shown in the image).  Since both triangles are right triangles, we can say they are similar by AA similarity.

Since they're similar, we can write a proportion.

HT / TV = JS / SV

Plugging in values:

5.8 / 4 = JS / 36

JS = 52.2

The wall is 52.2 feet tall.

The percentage of male workers who preferred a female boss increased at a rate of 0.1667% per year from 1974 to 1998. Using this information, we can predict that 9% of male workers would prefer a female boss in the year 1998.

This question involves linear relationships and prediction in mathematics. In this case, we're looking at an increase from 5% to 9% in male workers who preferred a female boss--this increase occurred over a period of 24 years (from 1974 to 1998). So, the rate of increase in male workers who preferred a female boss over those years was (9% - 5%) / 24 years = 0.1667% per year. Since the percentage was 5% in the beginning year 1974, we need to find the year when this percentage will become 9%. So, 9% = 5% + 0.1667% * (number of years from 1974). Solving this for the number of years gives approximately 24 years. Therefore, the year when 9% of male workers will prefer a female boss would be 1974+24 = 1998

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Answer:

  500

Step-by-step explanation:

The problem statement tells you ...

  300 = 0.60×voters

Dividing by the coefficient of the variable gives ...

  300/0.60 = voters = 500

500 students voted in the election.

Answer:

500

Step-by-step explanation:

Answer:

Step-by-step explanation:

372 + 1/4*372 = $465

$465 is her new savings and 33% of it is $153.45

$465 + $153.45 = $618.45

So yes she would have enough money to buy a plane ticket to alaska the cost $600

Answer:

Step-by-step explanation:

4π r²=144 π

r²=36

r=6 cm

Answer:

About 428 N

Step-by-step explanation:

Weight = 1,500 * 9.8 = 14,700 N

Density = Mass ÷ Volume

1,030 = 1,500 ÷ V

V = 1,500 ÷ 1,030  = 1.46 m^3.

Buoyant force = Density * g * V  

Buoyant force = 1,000 * 9.8 * (1,500 ÷ 1,030)

Buoyant force = 9,800 * (1,500 ÷ 1,030)  = 14,272 N.

Net force = 14,700 – [(9,800 * (1,500 ÷ 1,030)]

The upward normal force on a 1500 kg submerged hippo is approximately equal to its weight, calculated as its mass times the acceleration due to gravity (1500 kg × 9.81 m/s²), resulting in a force of 14715 N.

The question is asking about the upward normal force on a submerged hippo in a lake. To find this force, we must understand that the upward normal force that the ground (or in this case, the lake bed) exerts on the hippo is equal to the weight of the hippo, which is the product of the hippo's mass (m) and the acceleration due to gravity (g).

In equation form: Normal Force = m × g. Plugging in the values, we have a 1500 kg hippo and the acceleration due to gravity is approximately 9.81 m/s². Therefore, the upward normal force is:

Normal Force = 1500 kg × 9.81 m/s² = 14715 N.

This is the approximate value of the upward normal force exerted on the hippo standing on the bottom of the lake.

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Answer:

Our answer is $2000

Step-by-step explanation:

Short term capital loss = $1000

Long term capital loss = $4000

Taxable Income = $30000

Long term capital loss carryover to 2019 = ($1000 + $4000) - $3000 = $2000

Answer: Waters on 7th day

Step-by-step explanation:

If she waters everyday then days= 1,2,3,4,5,6,7,8,9

If she waters every other day= 1,3,5,7,9

If she waters every third day= 1,4,7,10,13

So the common day to all is either 1st day or 7th day.

Yo sup??

Since the two figures are similar therefore their sides are in proportion.

for the first one

factor=2/8=1/4

for the second

factor=10/4=5/2

Hope this helps.

Answer: 7

Step-by-step explanation:

Answer:

The first one.

Step-by-step explanation:

We can say lines L and K are parallel, because they have the same slope and different y intercepts.

This would mean they will always be moving in the same direction, hence causing them to never touch.

Answer:

n≅376

So sample size is 376.

Step-by-step explanation:

The formula we are going to use is:

[tex]n=pq(\frac{z_{\alpha/2}}{E})^{2}[/tex]

where:

n is the sample size

p is the probability of favor

q is the probability of not in favor

E is the Margin of error

z is the distribution

α=1-0.98=0.02

α/2=0.01

From cumulative standard Normal Distribution

[tex]z_{\alpha/2}=2.326[/tex]

p is taken 0.5 for least biased estimate, q=1-p=0.5

[tex]n=0.5*0.5(\frac{2.326}{0.06})^{2}\\n=375.71[/tex]

n≅376

So sample size is 376