True or false

1. 2⁴ × 2³ = 6⁷
____________ T or F

2. 1⁰ × 0¹ = 1
____________ T or F

3. 3⁴ > 4³
____________ T or F

4. 4⁰ + 5⁰ + 6⁰ = ( 4 + 5 + 6 )⁰
____________ T or F ​


please answer it

Answer:

$120.64

Step-by-step explanation:

Step one:'

given data

originally price fo microscope = $148.48

discount= 25%

tax= 6.25%

Step two:

the total amount paid for the microscope

1. Amount of the discount= 25/100*148.48

= 0.25*148.48

=$37.12

2. Amount of tax

= 6.25/100*148.48

= 0.0625*148.48

=$9.28

Step three:

The total amount is

= 148.48-37.12+9.28

=$120.64

Answer:

The price of a child ticket in dollars $8.00

Step-by-step explanation:

4÷1.84 means 4 over 1.84 (4/1.84) = 2.17

if u calculate 1.84 ÷ 4 (using calculator) the ans will be different bcauz it means 1.84 over 4 (1.84/4)

In conclusion, the rate of change of F with respect to t is F'(t) = 30[- 0.6 sin(t)] / [0.6 sin(t) + cos(t)]², and the rate of change of F with respect to t will be zero when t = nπ, where n is any integer except 0.

The given force is F = (µW)/(µ sin(t) + cos(t)), where µ = 0.6 and W = 50lb.

(a) Find the rate of change of F with respect to F'(t)

We are required to find the rate of change of F with respect to F'(t).

Differentiating the given equation, we get:

dF/dt = [d/dt (µW)]/[µ sin(t) + cos(t)] - [µW d/dt(µ sin(t) + cos(t))] / [µ sin(t) + cos(t)]²

Now, substituting the values of W and µ in the equation above, we get:

dF/dt = [d/dt (30)]/[0.6 sin(t) + cos(t)] - [(0.6)(50)(cos(t))] / [0.6 sin(t) + cos(t)]2²

On simplifying the above equation, we get:

dF/dt = 30[- 0.6 sin(t)] / [0.6 sin(t) + cos(t)]²

(b) When is this rate of change equal to zero-

We have the rate of change of F with respect to t as:

dF/dt = 30[- 0.6 sin(t)] / [0.6 sin(t) + cos(t)]²

The rate of change of F with respect to t will be zero when the numerator is zero.

So, - 0.6 sin(t) = 0 ⇒ sin(t) = 0

which implies t = nπ

where n is any integer, except 0.

Therefore, t ≠ 0.

In conclusion, the rate of change of F with respect to t is F'(t) = 30[- 0.6 sin(t)] / [0.6 sin(t) + cos(t)]2, and the rate of change of F with respect to t will be zero when t = nπ, where n is any integer except 0.

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Dante and Mia lost a total of 100 + 50 = 150 pennies.

Let's denote the number of pennies Dante initially had as "D" and the number of pennies Mia initially had as "M." According to the given information, we know that D + M = 350.

After Dante lost half of his pennies, he would have (1/2)D pennies remaining, and after Mia lost one-third of her pennies, she would have (2/3)M pennies remaining. It is stated that they both had an equal number of pennies after these losses.

Therefore, we can set up the following equation:

(1/2)D = (2/3)M

To simplify this equation, we can multiply both sides by 6 to eliminate the fractions:

3D = 4M

Now we have a system of equations:

D + M = 350
3D = 4M

We can solve this system to find the values of D and M. Multiplying the first equation by 4, we get:

4D + 4M = 1400

Substituting 3D for 4M from the second equation, we have:

4D + 3D = 1400
7D = 1400
D = 200

Substituting D = 200 back into the first equation, we find:

200 + M = 350
M = 150

So, Dante initially had 200 pennies, and Mia initially had 150 pennies.

To find out how many pennies they lost, we need to calculate the difference between their initial amounts and their final amounts:

Dante lost: 200 - (1/2)D = 200 - (1/2)(200) = 200 - 100 = 100 pennies
Mia lost: 150 - (2/3)M = 150 - (2/3)(150) = 150 - 100 = 50 pennies

Therefore, Dante and Mia lost a total of 100 + 50 = 150 pennies.

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Answer:

Step-by-step explanation:

Plot 213, −56, and −312 on the number line.

Answer:

Step-by-step explanation:

Let's solve your equation step-by-step.

7x+10=3x+13

Step 1: Subtract 3x from both sides.

7x+10−3x=3x+13−3x

4x+10=13

Step 2: Subtract 10 from both sides.

4x+10−10=13−10

4x=3

Step 3: Divide both sides by 4.

4x/4=3/4

x=3/4

Answer:

6.45kg

Step-by-step explanation:

there are 1000g in one kilogram

250g/1000g=0.25kg

4.2kg+2.25kg=6.45kg

Answer:

6.45kg

Step-by-step explanation:

First, let us convert all the values into grams.

Weight of a watermelon ⇒ 4.2 kg

Multiply by 1000 to convert it to grams.

Weight of a watermelon ⇒ 4200 g

Weight of a pumpkin ⇒ 2kg 250g

First, multiply 2kg by 1000 to convert it to grams and add it to 250 grams.

Weight of a pumpkin

⇒ ( 2 × 1000 ) + 250

⇒ 2000 + 250

⇒ 2250 g

Total Weight  :

To get the total weight, add the weights of the watermelon and pumpkin in grams.

Total weight ⇒ 4200g + 2250g

                     ⇒ 6450g

Now to convert the answer into kilograms, divide the answer by 1000.

⇒ 6450/1000 = 6.45kg

You will need 2 gallons of paint to paint the walls of the 20 ft by 20 ft room..

To determine the number of gallons of paint needed for the room, we need to calculate the total surface area of the walls.

First, calculate the area of one wall:
Area of one wall = height * length
Area of one wall = 10 ft * 20 ft
Area of one wall = 200 square feet

Since there are four walls in the room, we need to calculate the total area of all the walls:
Total area of walls = area of one wall * number of walls
Total area of walls = 200 square feet * 4 walls
Total area of walls = 800 square feet

Next, divide the total area of the walls by the coverage of one gallon of paint:
Gallons of paint needed = Total area of walls / Coverage of one gallon of paint
Gallons of paint needed = 800 square feet / 400 square feet per gallon
Gallons of paint needed = 2 gallons

Therefore, you will need 2 gallons of paint to paint the walls of the 20 ft by 20 ft room.

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To paint the walls of a 20 ft by 20 ft room with 10 ft high walls, you will need 2 gallons of paint.

To calculate the amount of paint needed to cover the walls of a 20 ft by 20 ft room, we first need to determine the total area of the walls.

The room has four walls, each with a height of 10 ft. Since the walls go all the way around the room, the total perimeter of the room is (20 ft + 20 ft + 20 ft + 20 ft) = 80 ft.

To find the total area of the walls, we multiply the perimeter by the height: (80 ft) * (10 ft) = 800 square feet.

Since a gallon of paint covers 400 square feet, we divide the total area of the walls by the coverage per gallon: 800 square feet ÷ 400 square feet/gallon = 2 gallons.

Therefore, you will need 2 gallons of paint to cover the walls of the 20 ft by 20 ft room.

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Where the line y = 3x + 5 cross the y-axis is at y = 5. Option D

It is crucial to note that the general formula for the equation of a iine is expressed as;

y = mx + c

The parameters are enumerated as;

To determine where the line of graph crosses the y-axis

Let's compare the equations

y = 3x + 5 and y = mx + c

Then, the intercept is 5

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Answer:

$6.36

Step-by-step explanation:

this is a system of equations problem. There are two main methods for this type of problem: elimination and substitution(I used both here). A-croissants, B-coffee.

The cost of an order of 1 croissant is $2.3 and 1 cup of coffee is $4.05.

We need to form the system of equations for the given statement.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let the cost of croissants be x and the cost of cups of coffee be y.

6 croissants and 3 cups of coffee costs $25.95

6x+3y=25.95-----(1)

1 croissant and 6 cups of coffee cost $26.70

x+6y=26.70-----(2)

(6x+3y)6=25.95×6

⇒36x+18y=155.7-----(3)

(x+6y)3=26.70×3

⇒3x+18y=80.1-----(4)

Subtract (4) from (3).

That is, 36x+18y-(3x+18y)=155.7-80.1

⇒33x=75.6

⇒x=2.3

Substitute x=2.3 in equation (1).

That is, 6(2.3)+3y=25.95

⇒3y=12.15

⇒y=4.05

Therefore, the cost of an order of 1 croissant is $2.3 and 1 cup of coffee is $4.05.

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The likelihood of obtaining three heads in a row when a coin is tossed three times is 0.125.

When a fair coin is tossed, there are two possible outcomes: heads (H) or tails (T). Each individual toss of the coin is an independent event, meaning that the outcome of one toss does not affect the outcome of subsequent tosses.

To find the likelihood of obtaining three heads in a row, we need to consider the probability of getting a head on each individual toss. Since there are two possible outcomes (H or T) for each toss, and we want to get heads three times in a row, we multiply the probabilities together.

The probability of getting a head on a single toss is 1/2, since there is one favorable outcome (H) out of two equally likely outcomes (H or T).

To get three heads in a row, we multiply the probabilities of each toss: (1/2) * (1/2) * (1/2) = 1/8 = 0.125.

Therefore, the likelihood of obtaining three heads in a row when a coin is tossed three times is 0.125.

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The p-value for this test is 0.007.

Explanation:

To find the p-value for this test, we need to use a standard normal distribution table or calculator. The test statistic is 2.48, which represents the number of standard deviations away from the null hypothesis mean (μ0) that the sample mean falls.

Since the alternative hypothesis (h1) is one-sided (μ > μ0), we need to find the probability of getting a test statistic as extreme or more extreme than 2.48 under the null hypothesis. This corresponds to the area to the right of 2.48 on a standard normal distribution.

Using a standard normal distribution table or calculator, we can find that the area to the right of 2.48 is approximately 0.007. This is the p-value for the test.

Interpreting the p-value: Since the p-value (0.007) is less than the significance level (α) of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the population mean (μ) is greater than μ0. In other words, the sample provides strong evidence that the true population mean is higher than the hypothesized value.

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The value which shows the true solution to the logarithmic equation solved below is 1.

Domain of a function is the set of all the possible input values which are valid for that function.

Range of a function is the set of all the possible output values which are valid for that function.

The given logarithmic equation is,

\(\log_2x+\log_2(x+7)=3\)

Use the addition property of log in above expression.

\(\log_2[x\times(x+7)]=3\)

Use the power rule property of log in above expression.

\([x\times(x+7)]=2^3\\x\times(x+7)=8\\x^2+7x-8=0\)

Solve the quadratic equation with the help of split the middle term method,

\(x^2+8x-1x-8=0\\x(x+8)-1(x+8)=0\\(x+8)(x-1)=0\\x=-8,1\)

Here, the two values of variable we get. One is positive and another is negative. As the logarithmic function is defined only for positive real number as its input.

Thus, the value which shows the true solution to the logarithmic equation solved above is 1.

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Answer:

1

Step-by-step explanation:

edge 2022

Answer:

Below

Step-by-step explanation:

68 x 157 = 10 676      to the nearest 100 would be 10700 ....the '7' next to the 6 in the 100s place dictates that you round the 6 UP to 7

Answer:

1167 of them are girls in the first situation.

1052 of them are boys in the second situation.

Step-by-step explanation:

Since there are 2723 students at the school and 4/7 of them are boys, the number of boys:

→ 2723 x \(\frac{4}{7}\) = 1556

The number of the girls = Total number of students - The number of boys

→ 2723 - 1556 = 1167

Since there are 2367 students at the school and 5/9 of them are girls, the number of girls

→ 2367 x \(\frac{5}{9}\) = 1315

The number of the boys = Total number of students - The number of girls

→ 2367 - 1315 = 1052

Samuel needs a total of 6 containers for his plan

The complete question is added as an attachment

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

1 cup of rubbing alcohol = 1/(1/2) = 2 shares

Also, we have

1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5

For the 2 shares calculated above, we have

2 shares = 17.5 * 2

Evaluate

2 shares = 35

Given that each can hold a maximum of 6 cups, the number of containers needed is

Container = 35/6

This gives

Container = 5.83

Round up

Container = 6

Hence, he needs 6 containers

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Answer:

$960

Step-by-step explanation:

The discount is 20%, so we need to find 80% of the original price:

\(.80 \times 1200 = 960\)

Answer:

128  *  [1 / (x^7)]

Step-by-step explanation:

first we simplify

(-2)^-7 (x^-7)

128x^-1

now we use the exponential ruleset to make the negative exponent a positive one

128  *  [1 / (x^7)]

Answer:

-w^-7/128 (fraction form)

Step-by-step explanation:

1.  Distribute exponent

(-2w)^-7

(-2)^-7w^-7

2. Evaluate the exponent

(-2)^-7w^-7

-1/128w^-7

3. Combine multiplied terms into a single fraction

-1/128w^-7

-1w^-7/128

4. Solution

-w^-7/128

Answer:

It is the second one: Solve the first equation for x.

Step-by-step explanation:

The gradient vector Vf(x, y) and evaluate it at a specific point. In this case, at point P = (7, -1), Vf(7, -1) will be determined. Therefore, the directional derivative of the function at point P in the direction of Q is 0.

The gradient vector Vf(x, y) represents the vector of partial derivatives of a function. For f(x, y) = -√2, the gradient vector is Vf(x, y) = (-∂f/∂x, -∂f/∂y) = (0, 0) since the function is constant.

To determine Vf(x, y) at the point P = (7, -1), we substitute the values into the gradient vector: Vf(7, -1) = (0, 0).

To find a unit vector in the direction of PQ, we calculate the vector PQ = Q - P = (-9 - 7, 11 - (-1)) = (-16, 12). Normalizing this vector, we divide it by its magnitude to obtain the unit vector: u = (-16/20, 12/20) = (-4/5, 3/5).

For the directional derivative of the function at point P in the direction of Q, we take the dot product of the gradient vector Vf(7, -1) = (0, 0) and the unit vector u = (-4/5, 3/5): Vf(7, -1) · u = (0 · (-4/5)) + (0 · (3/5)) = 0.

Therefore, the directional derivative of the function at point P in the direction of Q is 0.

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Answer:

C. 904.32 cubic units

Step-by-step explanation:

the volume = π×r²×h

= 3.14 × 6²×8

= 3.14×288

= 904.32

Answer:

112 students

Step-by-step explanation:

From this problem, we can gather that 80% of the students are not performing.

140*0.8=112

Answer:

The population of Hawks and other species would likely start to edge off.

Step-by-step explanation:

Commonly, a Food Chain is dependent on all the parts of it sataying at a perfect point. If the food that the Snakes eat starts to run out, more of them will die off. With less Snakes, the Hawks will then have less food, and that continues throughout the chain. The same thing would happen if there was too much food, except instead of the populations of species dying off, the Snake population would spike.

Answer:
I believe it is Option C.

Step-by-step explanation:

There has only been one single tie since the passing of the 12th Amendment. It is a very low chance for a possible tie to take place, so they would have no reason to ensure it doesn't happen as it's already unlikely, ruling out option D. Giving two people the same rank would definitely make a difference as you are basically adding not 1, but two votes. Though it would even the count out, each person would gain 1 point, so it would make a difference. Option B is ruled out. This also potentially explains debunking A as there's no possible way to plan a tie to that extent. Again. ties happen very rarely, so it would be unlikely that voting for both candidates would impact the choice at all.