A baker has 15 cups of flour. He sets aside 4 cups, and uses the rest for a cookie recipe that calls for 1/2 cup of flour. How many batches of cookies can the baker make?

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:

The answer is D.

Step-by-step explanation: A monomial is an algebraic expression that consists of one term. D consists of 2 terms and is considered a binomial.

Graph A is the correct representation, as it aligns with the functions f(x) and g(x), resulting in the accurate intersection point (2, 4). Graph B does not accurately represent the functions based on the reported intersection point (4, 1).

The correct graph can be determined by analyzing the given functions and the specified intersection points. The functions are f(x) = -3/4 * x^2 + 3x + 1 and g(x) = 2x, and the reported intersection points are (2, 4) for graph A and (4, 1) for graph B.

To verify the accuracy, substitute the x-values into both functions:

Graph A (Intersection at (2, 4)):

f(2) = -3/4 * (2)^2 + 3 * 2 + 1 = 4

g(2) = 2 * 2 = 4

Both functions align, confirming the correctness of the reported intersection point.

Graph B (Intersection at (4, 1)):

f(4) = -3/4 * (4)^2 + 3 * 4 + 1 = 1

g(4) = 2 * 4 = 8

There is a discrepancy here, as the y-values do not match. Therefore, graph B does not accurately represent the functions f(x) and g(x).

In conclusion, graph A is correct since it accurately reflects the given functions and results in the reported intersection point (2, 4).

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.

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:

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

This is a comparison problem involving rates. We multiply the rate of draining by the time and subtract the result from the initial amount, which gives us the amount of water after that time.

This problem is considerate a comparison problem that involves rates of draining water from two pools. In these cases, it's crucial to keep the rates and the initial amounts separate to correctly solve the problem.

The first pool is initialy with 3700 liters of water and the draining rate is 31 liters per minute. The second pool from the start has 4228 liters and is being drained at a rate of 42 liters per minute.

To know the amount of water in each pool after any given time in minutes, we would multiply the rate by that time, and subtract the result from the initial amount of water.

For example, if we wanted to find out how much water was left after 10 minutes, we would do the following calculations:

Therefore, after 10 minutes, the first pool had 3700 liters and the second one had 3828 liters of water.

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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:

0 N

Step-by-step explanation:

We are given that

[tex]m_1=7 kg[/tex]

[tex]m_2=0.7 kg[/tex]

Total mass =[tex]m_1+m_2=7+0.7=7.7 Kg[/tex]

We have to find the magnitude of the normal force with which the bottom cube is acting on the top cube.

When both cube are fall freely then

g=[tex]0m/s^2[/tex]

Then, the weight=[tex]mg=7.7\times 0=0 N[/tex]

The direction of weight is downward.

We know that

Normal force is equal to weight and act in opposite direction of weight.

When the weight is zero N then

The magnitude of the normal force with which the bottom cube is acting on the top cube=0 N

Answer:

Step-by-step explanation:

4π r²=144 π

r²=36

r=6 cm

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:

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:

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:

(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.

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:

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:

[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:

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

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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:

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

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.

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: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".

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Answer:

3(x-6)(x+2) and (3x+6)(x-6)

Step-by-step explanation:

The other two answers are wrong because the value for their x will be positive.

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

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:

The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.

Step-by-step explanation:

It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.

Let the acute angle be m∠A.

For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.

The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,  

                                 [tex]Sin\ 45^{o} =Cos\ 45^{o} = \frac{1}{\sqrt{2} }[/tex]

So for acute angle 45° the ratio of Sin 45° and Cos 45° is:

                                         [tex]\frac{Sin\ 45^{o}}{Cos\ 45^{o}} = \frac{\frac{1}{\sqrt{2} } }{\frac{1}{\sqrt{2} } } = 1[/tex]

Hence one of the angles of a triangle is, m∠A = 45°.

Comparing with the options provided the triangle is,

Triangle ABC that has angle measures 45°, 45° and 90°.

Thus, the provided triangle is a right angled isosceles triangle, since it has two similar angles.

Answer:

IT'S the second option

Step-by-step explanation:

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:

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.