Tyler is 8 years old his sister Olivia is 4 years less than twice his age write a numerical expression for Olivia’s age

Answer:

7c1 is an algebraic expression that evaluates to 47. The expression is made up of two terms, 7 and c1. The letter c is a variable and the number 1 represents the exponent of the variable. Therefore, 7 multiplied by the c to the power of 1 is equal to 7 times c, which is equal to 47.

6p4 is an algebraic expression that evaluates to 6,040. The expression is made up of two terms, 6 and p4. The letter p is a variable and the number 4 represents the exponent of the variable. Therefore, 6 multiplied by the p to the power of 4 is equal to 6 times p to the fourth power, which is equal to 6,040.

A lead atom is 200 times heavier than a hydrogen atom.

To determine how many times heavier a lead atom is compared to a hydrogen atom, we can calculate the ratio of their masses.

Mass of hydrogen = 1.7 × 10⁻²⁴ grams

Mass of lead atom = 3.4 × 10⁻²² grams

To find the ratio of their masses, we divide the mass of the lead atom by the mass of the hydrogen atom:

Ratio = 3.4 × 10⁻²² /  1.7 × 10⁻²⁴

= (3.4 / 1.7)× 10⁻²² / 10⁻²⁴

= 2×10²

= 200

Therefore, a lead atom is 200 times heavier than a hydrogen atom.

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The approximate mass of a hydrogen atom is 1.7*10^-24 grams. The mass of a single lead atom is approximately 3.4*10^-22 grams. How many times heavier is a lead atom than a hydrogen atom.

A. 5 times heavier

B. 20 times heavier

C. 50 times heavier

D. 200 times heavier

Answer:

4π cm

Step-by-step explanation:

A minute hand travels a full revolution along a circular path in 60 minutes

The distance from the center to the tip of the minute hand = 8 cm

We can consider the movement of the minute hand as being on the circumference of  a circle with radius = 8 cm

Circumference = 2π · r

=  2π · 8

= 16π

I5 minutes = 15/60 = 1/4th

So in 15 minutes the minute hand will cover only 1/4th of the full circle

Therefore distance traveled by tip of minute hand

= 1/4 x 16π = 4π cm

The probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.

Calculating the standard error of the mean (SE) using the formula:

SE = σ / sqrt(n)

where σ is the standard deviation and n is the sample size.

SE = 1.02 / sqrt(45) ≈ 0.1522

We can calculate the z-score using the formula:

z = (x - μ) / SE

where x is the observed mean and μ is the claimed mean.

z = (1.73 - 1.8) / 0.1522 ≈ -0.4582

Using a standard normal distribution table or a calculator, we find that the probability is approximately 0.3231.

Therefore, the probability that the mean weight loss after one week on the pill for a random sample of 45 individuals will be 1.73 pounds or less is approximately 0.3231, or 32.31%.

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Answer:

[tex]3.23*10^{16}[/tex]

Step-by-step explanation:

Just multiply. You have to do:

[tex](1.12*10^7)*(2.88*10^9)\\=3.23*10^{16}[/tex]

Answer:

The Answer to This question Is x + 5 So Basically 5

Part A:  At her current rate, the distance Amy can ride her bike within 12 minutes is A. 1.6 miles.

Part B: Sebastian can ride his bike for  C: 7.5 miles in 1 hour.

Part C: The time it will take for one to wait is B: Amy will have to wait 1.5 minutes for Sebastian.

Part A:

To find the distance Amy can ride her bike in 12 minutes, we set up a proportion based on her current rate.

Amy's rate: 4 miles / 30 minutes = x miles / 12 minutes

Cross-multiplying:

30x = 4 * 12

30x = 48

Dividing both sides by 30:

x = 48 / 30

x ≈ 1.6

So, Amy can ride her bike at 1.6 miles in 12 minutes.

Part B:

To find the distance Sebastian can ride his bike in 1 hour, convert the time to minutes first.

1 hour = 60 minutes

Sebastian's rate: 3 miles / 24 minutes = x miles / 60 minutes

Cross-multiplying:

24x = 3 * 60

24x = 180

Dividing both sides by 24:

x = 180 / 24

x ≈ 7.5

Therefore, Sebastian can ride his bike at 7.5 miles in 1 hour.

Part C:

Amy's home to  Park = 3 miles,

Park to Sebastian's home = 3 miles.

Amy's rate = 4 miles in 30 minutes, equivalent to 1 mile in 7.5 minutes.

Sebastian's rate = 3 miles in 24 minutes, equivalent to 1 mile in 8 minutes.

Then, we estimate the time it takes for each to cover a distance of 3 miles.

Amy:

Time = Distance / Rate = 3 miles / (2/15 miles/minute)

= 3 * (15/2) minutes

= 22.5 minutes

Sebastian:

Time = Distance / Rate = 3 miles / (1/8 miles/minute)

= 3 * 8 minutes

= 24 minutes

Since Amy= 22.5 mins and Sebastian takes 24 mins,

24 - 22.5 = 1.5

Hence, Amy will have to wait 1.5 minutes for Sebastian.

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Answer:

3/10

Step-by-step explanation:

7/10 – 2/5

=7/10 – 4/10

=(7–4)/10

=3/10

Answer:

0.3

Step-by-step explanation:

Step-by-step explanation:

Part A:

To find the composite function, we need to plug in the expression for s(w) into f(s):

f(s(w)) = 2s(w) + 30

= 2(40w) + 30

= 80w + 30

Therefore, the composite function that represents how many flowers Lily can expect to bloom over a certain number of weeks is f(s(w)) = 80w + 30.

Part B:

The units of measurement for the function f(s(w)) are the same as the units of measurement for f(s) and s(w). From the given information, we know that s(w) represents the number of seeds planted per week and f(s) represents the number of flowers bloomed based on the number of seeds planted. Thus, the units of measurement for f(s(w)) are "flowers" per week.

Part C:

To evaluate the composite function f(s(w)) for 35 weeks, we need to substitute w = 35 into the expression we found in Part A:

f(s(35)) = 80(35) + 30

= 2,830

Therefore, Lily can expect 2,830 flowers to bloom after planting 40 seeds per week for 35 weeks.

Answer: c

Step-by-step explanation:

i took the test

The surface area of the prism given is 362 m².

Given is a prism.

We have to find the total surface area of the prism.

The given prism has to be divided in to various other known figures to find the total area.

By drawing a line vertically through the top of the prism, we get two rectangular prism.

Surface area of a rectangular prism = 2 [lw + wh + lh], where l, w and h are length, width and height respectively.

Surface area of big rectangular prism = 2[(6 × 6) + (6 × 7) + (6 × 7)]

                                                               = 240 m²

Surface area of smaller rectangular prism = 2[(3 × 4) + (4 × 7) + (3 × 7)]

                                                                      = 122 m²

Total area of the prism = 240 m² +  122 m²

                                      = 362 m²

Hence the surface area is 362 m².

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ok, let's assume the rate is 0.075 per minute, if we convert that to percentage that'd be 0.075*100 or 7.5% per minute, so we can assume the bread is cooling off at 7.5% per minute after coming out of the oven at 340°F and we need it at 80°F so we can slice it and put some butter on it.

now, we can look at this from a Decay standpoint and say

we have a temperature of 340°F, decaying at 7.5% per minute, how long before it turns into 80°F?

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 80\\ P=\textit{initial amount}\dotfill &340\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=minutes \end{cases}[/tex]

[tex]80 = 340(1 - 0.075)^{t}\implies \cfrac{80}{340}= 0.925^t\implies \cfrac{4}{17}=0.925^t \\\\\\ \log\left( \cfrac{4}{17} \right)=\log(0.925^t)\implies \log\left( \cfrac{4}{17} \right)=t\log(0.925) \\\\\\ \cfrac{ ~~ \log\left( \frac{4}{17} \right) ~~ }{\log(0.925)}=t\implies 18.56\approx t\qquad \textit{almost 19 minutes}[/tex]

Answer:

[tex]f(x) = (x - 4)(x + 3) [/tex]

[tex]f(x) = {x}^{2} - x - 12[/tex]

Note that based on the volume  calculations,  the manager's statement is NOT correct. The given area of 2m × 2m is insufficient to store all 80 crates.

To verify if the manager's statement is correct, we need to derive the volume of each crate and the total volume required to store all 80 crates.

Volume = Length × Width × Height

Recall that

Length (L) = 690 mm

Width (W) = 445 mm

Height (H) = 180 mm

Thus, the Volume of one crate is

Volume = 690 mm × 445 mm × 180 mm

Converting mm to meters we have,

Volume = (690 / 1000)  × (445 / 1000)  × (180 / 1000)

= 0.690  × 0.445 × 0.180

= 0.055269 m³

Next , we calculate the total volume required for 80 crates as

Total Volume = Volume of one crate × Number of crates

= 0.055269 m³ × 80

= 4.42152 m³

Recall that the manager stated that all 80 crates can be packed in a 2m × 2m area in the store room.

Since area of store room is

Area = 2 m × 2 m

Area = 4 m²

Comparing the total volume required (4.380208 m³) with the available area (4 m²), we see that the volume exceeds the area. Tus, the manager's statement is incorrect.

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Full question:

Manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.​

See attached Image.

The probability that we will get a lead role, given that we are chosen to be in the play is 0.7.

We have,

Probability is the ratio that shows the likelihood of an event occurring from a given set of possible events.

We can find the required probability below:

The probability that we will be chosen for the play is 0.5.

The probability that we will get the lead role is 0.2.

In this situation, the probability can be found by adding the probability of being chosen and the probability that we will get the lead role.

The probability that we get a lead role, = The probability that we will be chosen for the play + The probability that we will get the lead role

= 0.5 + 0.2

= 0.7

The probability of us getting a lead role given that we have already been chosen for the play is found to be 0.7. The correct answer is option C.

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complete question:

You are trying out for the school play. The probability that you are chosen to

be in the play is 0.5. The probability that you get a lead role is 0.2. What is the

probability that you get a lead role, given that you are chosen to be in the

play?

O A. 0.5

Oo oo

O B. 0.4

O c. o7

O D.0.3​

Answer:

25/51

Step-by-step explanation:

If the first card was a heart, we've drawn one red card already.

The ratio of black to red cards in the deck is now 26:25.

On the second draw, there will be only 51 cards to choose from, rather than 52 because you have already taken out a card. Therefore, you only have a 25/51 chance of drawing a red card compared to the 26/52 or 1/2 chance on the first draw.

Answer is 25/51.

Answer:

Measure of angle HEK is: 85°.

Step-by-step explanation:

Given that point E is the center of the protractor, we have:

angle HEJ = 55° (EH points to 55 degrees)

angle JEK = 30° (EK points to 30 degrees)

Since angle HEJ and angle JEK meets at a point E, then we can find angle HEK by summing up the two angles:

angle HEK = angle HEJ + angle JEK

angle HEK = 55° + 30°

angle HEK = 85°

Answer:

x-intercept = -7

y-intercept = 1

rate of change = 1.25

Step-by-step explanation:

X and Y intercept are pretty to find.

Rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex]

So for our case it will be [tex]\frac{-0.75-(-2)}{-8-(-9)}[/tex]

The answer will be 1.25

There are 1440 minutes in a day (24 hours x 60 minutes = 1440 minutes).

To convert 4320 minutes to days, divide 4320 by 1440:

4320 ÷ 1440 = 3

Therefore, 4320 minutes is equivalent to 3 days.

Answer: 3 days

Step-by-step explanation:

The distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles. Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).

1. Find the distance from the satellite to the points of tangency Solution: Firstly, we need to draw a rough diagram of the scenario to easily understand it. Consider a satellite revolving around an alien planet in a synchronous orbit 18,000 miles above its surface.

We can see that B and D are the points of tangency of the satellite signal with the planet, and C is the center of the planet. Hence, the figure will look like the following: Image Source: Synchronous Orbit - Wikimedia Commons Now, we need to find the distance from the satellite to the points of tangency.

Hence, the distance from the satellite to the points of tangency, B and D, is 61861.9 miles (approximately 61862 miles).2. Find the percentage of the planet's equator within range of the satellite's signal Solution: We can see that the planet's equator can be represented by a circle with a radius of 3500 miles. Hence, the circumference of the circle would be 2π × 3500 miles ≈ 21991.5 miles.

We know that the satellite's signal can be received directly up to a distance of 61862 miles from it. Hence, the length of the portion of the equator within range of the satellite's signal would be twice the distance from the satellite to the point of tangency, which is 2 × 61862 ≈ 123724 miles. Now, we need to find the percentage of the planet's equator within range of the satellite's signal.

Hence, we need to find the time taken for the satellite signal to reach points B and E. We can see that the distance from the satellite to point B is 61862 miles and the distance from the satellite to point E is 3500 miles. Hence, the time taken for the satellite signal to reach point B would be: Time taken to reach point B = Distance / Speed = 61862 / 186000 ≈ 0.332 seconds Now, we need to find the time taken for the satellite signal to reach point E.

Hence, the time difference between the satellite signal reaching points B and E is approximately 0.07 seconds.4. Find the speed of the satellite Solution: We know that the satellite takes 36 hours to complete one revolution around the planet along with the point directly below it on the planet's surface. Hence, we need to find the distance travelled by the satellite in 36 hours to find its speed.

We can see that the distance travelled by the satellite in one revolution is equal to the circumference of the circle with a radius of 3500 miles, which is 2π × 3500 miles ≈ 21991.5 miles. Hence, the distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles.

Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).

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The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

Your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.

Since the final exam counts for 15% of the course grade, the weighted average can be calculated as follows:

Weighted average = (0.85 × 80%) + (0.15 × final exam score)

If we assume that your friend wants to get the highest possible grade, then they would need to get a perfect score on the final exam, which would be 100%.

Plugging this into the equation above, we get:

Weighted average = (0.85 × 80%) + (0.15 × 100%) = 83%

Therefore, the best course grade your friend can earn is 83%.

We can set up an equation where x is the minimum score needed on the final exam:

Weighted average = (0.85 × 80%) + (0.15 × x) = 75%

Simplifying this equation, we get:

0.85 × 80% + 0.15x = 75%

68% + 0.15x = 75%

0.15x = 7%

x = 46.67%

Therefore, your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.

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The reason for not applying method of addition and subtraction on first and third term shown below.

The reason why the method of addition and subtraction cannot always be applied to convert a trinomial with exact roots in the first and third terms into a perfect square trinomial is because the second term may not be a perfect square or a multiple of the square root of the first term multiplied by the square root of the third term.

In order to convert a trinomial into a perfect square trinomial using the method of addition and subtraction, the coefficient of the second term must be twice the product of the square root of the first term and the square root of the third term. If this condition is not met, the trinomial cannot be transformed into a perfect square trinomial using this method.

Therefore, it is important to consider the coefficients and terms of the trinomial to determine if the method of addition and subtraction can be applied successfully.

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The proof that the value of x is 38° is shown below

From the question, we have the following parameters that can be used in our computation:

ABDE is a parallelogram.

The measure of the angle opposite the vertex x is

Angle = 180 - 68

Evaluate the like terms

So, we have

Angle = 112

Also, we have

B = 68

AB = AC

So, we have

y = 180 - 68 - 68

y = 44

Using the above as a guide, we have the following:

x + 44 = 82

So, we have

x = 82 - 44

Evaluate

x = 38

Hence, we have shown that the value of x is 38°

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The probability of the point being in region A is 0.5294.

The area of the entire figure can be found by adding the areas of the four triangles:

Area of entire figure

= Area of triangle ABC + Area of triangle ACD + Area of triangle ABD + Area of triangle BCD

= (1/2)(5)(3) + (1/2)(3)(4) + (1/2)(4)(3) + (1/2)(3)(4)

= 7.5 + 6 + 6 + 6

= 25.5 square inches

Similarly, the area of region A can be found by adding the areas of triangles ABC and ABD:

Area of region A

= Area of triangle ABC + Area of triangle ABD

= (1/2)(5)(3) + (1/2)(4)(3)

= 7.5 + 6

= 13.5 square inches

Therefore, the probability of the point being in region A is:

P(A) = Area of region A / Area of entire figure

P(A) = 13.5 / 25.5

P(A) = 0.5294

So the probability of the point being in region A is 0.5294.

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The term (x - 1) is a factor of both of the given polynomials:

x² + x - 2

2x² - 5x + 3

If (x - a) is a factor of a polynomial p(x), then x = a is a zero of the polynomial, which means that:

p(a) =0.

So, if x - 1 is a factor of any of the given polynomials, then we need to evaluate them in x = 1 and check if we get zero.

a) x² + x - 2

Evaluate it in x = 1.

1² + 1 - 2 = 0

it is zero, so (x - 1) is a factor.

b) 2x² - 5x + 3

Evaluating this in x = 1.

2*1² - 5*1 + 3

2 - 5 + 3 = 0

(x - 1) is a factor.

Then the correct option is the last one, it is a factor of both polynomials.

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