Peter has 100$. The price of a watch is 60$. If Peter gets 25% discount,can he buy 2 watches?

what is this ..........

:-/

Answer:

3st + 8s + 16t

Step-by-step explanation:

Let's simplify step-by-step.

5st+8s+9t−2st+7t

=5st+8s+9t+−2st+7t

Combine Like Terms:

=5st+8s+9t+−2st+7t

=(5st+−2st)+(8s)+(9t+7t)

=3st+8s+16t

Answer:

no

Step-by-step explanation:

28x+17=157   Subtract 17 on both sides.

       -17  -17

28x=140

x=5

5 does not equal -10, so -10 is not a solution to the equation 28x+17=157.

Hope this helps!! Have a great day :)

The input value that produces the same output value for f(x) and g(x) on the graph is x = 1.To find the input value that produces the same output value for both functions, we need to determine the x-coordinate of the point(s) where the two lines intersect.

These points represent the values of x where f(x) and g(x) are equal.

The line labeled f(x) passes through the points (-2, 4), (0, 2), and (1, 1). Using these points, we can determine the equation of the line using the slope-intercept form (y = mx + b). Calculating the slope, we get:

m = (2 - 4) / (0 - (-2)) = -2 / 2 = -1

Substituting the point (0, 2) into the equation, we can find the y-intercept (b):

2 = -1(0) + b

b = 2

Therefore, the equation for f(x) is y = -x + 2.

Similarly, for the line labeled g(x), we can use the points (-3, -3), (0, 0), and (1, 1) to determine the equation. The slope is:

m = (0 - (-3)) / (0 - (-3)) = 3 / 3 = 1

Substituting (0, 0) into the equation, we can find the y-intercept:

0 = 1(0) + b

b = 0

Thus, the equation for g(x) is y = x.

To find the input value that produces the same output for both functions, we can set the two equations equal to each other and solve for x:

-x + 2 = x

Simplifying the equation:

2x = 2

x = 1.

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Answer:

56fifjjfiggitrireieisixii3eiirr

Answer:

Length = 33 cm

width = 11 cm

Step-by-step explanation:

a = 3w           ⇒ eq. 1

88 = 2(a+w)   ⇒ eq. 2

a = length

w = width

then:

replacing the value of the eq. 1 on the eq. 2

88 = 2(3w + w)

88/2 = 4w

44 = 4w

w = 44/4

w = 11 cm

from the eq. 1

a = 3w

a = 3*11

a = 33cm

Check:

perimeter = 88 = 2(a+w)

88 = 2(33+11)

88 = 2*44

a. R(3) represents the amount of rain measured by the rain gauge after 3 hours since it started raining.

b. R(0.5) represents the amount of rain measured by the rain gauge after 0.5 hours (30 minutes) since it started raining.

A function is an expression or relationship that involves one or more variables. It has several inputs and outputs. Each input has a single output. The function describes how the inputs relate to the output.

1)

a. R(3) represents the amount of rain measured by the rain gauge after 3 hours since it started raining.

b. R(0.5) represents the amount of rain measured by the rain gauge after 0.5 hours (30 minutes) since it started raining.

2)

a. R(6) = 37 represents that after 6 hours since it started raining, the amount of rain measured by the rain gauge was 37 millimeters.

b. R(90) = R(120) represents that the amount of rain measured by the rain gauge 90 minutes (1.5 hours) after it started raining was the same as the amount of rain measured by the rain gauge 120 minutes (2 hours) after it started raining.

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Answer:

22

Step-by-step explanation:

1 Simplify 14-6 to 8.

78-2^4 ÷ 8 × 28

2 Simplify 24 to 16.

78 - 68 ÷ 18 x 28

3 Simplify 16 ÷ 8 to 2.

78-2 × 28

4 Simplify 2 x 28 to 56.

78 - 56

5 Simplify.

22

Answer:

1.07 =)

Step-by-step explanation:

To determine how long it will take the Baxter boys to prepare 131 papers, we can use the concept of rate and proportion.

It will take approximately 11 minutes and 14 seconds (to the nearest minute) for the Baxter boys to prepare 131 papers. Given that the Baxter boys can prepare 35 papers in 3 minutes, we can set up a proportion to solve for the time it will take to prepare 131 papers.
First, let's set up the proportion using the information given about the rate of working:
35 papers / 3 minutes = 131 papers / x minutes
To solve for x, we can cross-multiply and then divide:
35 * x = 3 * 131
35x = 393
x = 393 / 35
x ≈ 11.229
Therefore, it will take approximately 11 minutes and 14 seconds (to the nearest minute) for the Baxter boys to prepare 131 papers.

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The set of points in space whose coordinates satisfy a given combination of equations and inequalities can be described by a geometric shape or region in 3-dimensional space.

Enumerate the collection of spatial points whose coordinates fulfil the specified set of equations and inequalities.

The equations and inequalities will define the properties of the region, such as its shape, size, and location.

For example, if we have the equation x + y + z = 3 and the inequality x^2 + y^2 <= 1, the set of points that satisfy these conditions would be the points on or inside a sphere of radius 1 centered at the point (0,0,-1) in the x-y plane, and points on the plane x+y+z = 3.

Another example, if we have the equation x + y = 4 and the inequality y >= 2x-5, the set of points that satisfy these conditions would be the points on the line x+y = 4, above or on the line y = 2x-5.

It's important to note that the type of shape or region that is formed by the equations and inequalities will depend on the specific equations and inequalities being used and the number of variables in the problem.

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Answer:

19

Step-by-step explanation:

I used my fingers and toes

Total distance traveled in the first second by the particle is 0 meters.

We need to integrate the velocity function from t=0 to t=1.

Distance traveled by the particle in first second is:

Step 1: Write down the given velocity function: v(t) = 2t - 1

Step 2: Integrate the velocity function with respect to time (t) from 0 to 1:

∫(2t - 1) dt from 0 to 1

Step 3: Find the antiderivative of the function:

Antiderivative: (2t²/²) - t + C = t² - t + C

Step 4: Evaluate the antiderivative at the limits 0 and 1:

[t² - t] from 0 to 1
= (1² - 1) - (0² - 0)
= (1 - 1) - (0)
= 0

Step 5: Take the absolute value of the result, as distance is always positive:

Total distance traveled in the first second = |0| = 0 meters

So, the total distance traveled by the particle in the first second is 0 meters.

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Answer:

30ft

Step-by-step explanation:

1530ft2 divided by 51ft.

The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(2, 14) and C(0, 5).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(2 + 0) / 2, (14 + 5) / 2]

(x, y) = (2/2, 19/2)

(x, y) = (1, 9.5)

The coordinates of the midpoint of a segment with the given endpoints will be (1, 9.5).

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Answer:

The two numbers are 8 and 5.

Step-by-step explanation:

Let consider x and y to be these two numbers.

So;

(x) * (y) = 40 ---- (1)

x + y     = 13 ----- (2)

From (2), let x =  13 - y

Then;

(13 - y) * y = 40

13y - y² = 40

13y - y² - 40 = 0

-y² + 13y - 40 = 0

Multiply through by (-)

y² - 13y + 40 = 0

By factorization;

(y - 8) (y - 5) = 0

y = 8 or  y = 5

CHECK:

8 * 5 = 40

8 + 5 = 13

Therefore, the two numbers are 8 and 5.

To find the answer, we need to identify the quartiles of the data set and use them to construct the box plot.

First, we need to order the data set in increasing order:

10, 15, 20, 25, 30, 35, 40, 45, 50, 55

Next, we need to find the median (Q2) of the data set. Since we have an even number of data points, we take the average of the two middle values:

Q2 = (25 + 30) / 2 = 27.5

This value represents the median of the data set.

To find Q1 and Q3, we divide the data set into two halves:

10, 15, 20, 25, 30 | 35, 40, 45, 50, 55

Q1 is the median of the lower half:

Q1 = (15 + 20) / 2 = 17.5

Q3 is the median of the upper half:

Q3 = (45 + 50) / 2 = 47.5

We can now use this information to construct the box plot:

     |         -------

     |        /

     |    -------

     |   /

     |-------

     |         10    20    30    40    50

            Q1          Q2         Q3

The box represents the middle 50% of the data (from Q1 to Q3), while the whiskers represent the minimum and maximum values that are not outliers.

Since we want to find the paint time for a student who is slower than 75% of the other students, we need to look at the upper quartile (Q3) of the data set. 75% of the data is contained between Q1 and Q3, so a student who is slower than 75% of the other students would have a paint time greater than Q3.

Therefore, the answer is 46 minutes, which is greater than Q3 (47.5 minutes).

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The alternative theorem states that if "p" is a prime number and "a" is a positive integer, then \(a^{(p)}\) is congruent to "a" modulo p. This theorem can be derived from Fermat's Little Theorem.

Fermat's Little Theorem states that if "p" is a prime number and "a" is an integer not divisible by p, then \(a^{p-1}\) is congruent to 1 modulo p. To derive the alternative theorem, we can start by applying Fermat's Little Theorem to the case where "a" is not divisible by p, resulting in \(a^{p-1}\) ≡ 1 (mod p).

Now, consider the case where "a" is divisible by p. In this scenario, "a" can be written as a = kp, where k is a positive integer. Substituting this into the alternative theorem, we have \((kp)^p\) ≡ kp (mod p). Expanding the left side using the binomial theorem, we get \(k^p * p^{p-1}\) ≡ kp (mod p).

Since "p" is a prime number, p^p-1 is congruent to 1 modulo p by Fermat's Little Theorem. Therefore, the equation simplifies to \(k^p\)k^p ≡ kp (mod p). We can cancel the common factor of p on both sides, giving \(k^p\) ≡ k (mod p). Finally, recognizing that k is a positive integer, we conclude that this congruence is valid for any positive integer k.

Hence, we have derived the alternative theorem, which states that if "p" is a prime number and "a" is a positive integer, then \(a^{(p)}\) is congruent to "a" modulo p, regardless of whether "a" is divisible by p or not.

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Hector and Gabrielle will have $638.45 in their savings account after two years of earning 13% interest compounded annually. They will be able to spend up to this amount on their trip.

To solve this problem, we need to use the formula for compound interest:

A = \(P(1 + r/n)^{(nt)\)

where:

A = the final amount

P = the initial deposit

r = the annual interest rate as a decimal

n = the number of times interest is compounded per year

t = the time in years

In this case, we have:

P = $500.00

r = 13% = 0.13 (as a decimal)

n = 1 (compounded annually)

t = 2 years

So, we can plug these values into the formula:

A = $500.00(1 + 0.13/1)²

A = $500.00(1.13)²

A = $500.00(1.2769)

A = $638.45

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Answer:

2 20/69

Step-by-step explanation:

Answer:

2 12/11

Step-by-step explanation:

7 9/6 / 2 3/4

34/11

(a)The probability that the mean price for a sample of 40 federal income tax returns is within $16 of the population mean is 0.6884, (b)The probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean is 0.7805. (c) The probability that the mean price for a sample of 81 federal income tax returns is within $16 of the population mean is 0.8502. (d) The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean

The solution to the given problem is as follows:A) For sample size of 40 Sample size, n=40Sample Mean, x = $273 Standard deviation of the population, σ= $100. Sampling Error = Standard error of mean = σ/√n = 100/√40 = $15.8114 therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.0 1)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/15.81) - P(Z < (256.99 - 273)/15.81)P(Z < 1.012) - P(Z > -1.012) = 0.8453 - 0.1569 = 0.6884. (B) For sample size of 60, sample size, n=60 sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√60 = $12.9155. therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01). Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/12.92) - P(Z < (256.99 - 273)/12.92)P(Z < 1.2389) - P(Z > -1.2389) = 0.8907 - 0.1102 = 0.7805.

C) For sample size of 81Sample size, n=81, sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√81 = $11.111. Therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/11.11) - P(Z < (256.99 - 273)/11.11)P(Z < 1.4403) - P(Z > -1.4403) = 0.9251 - 0.0749 = 0.8502.D) To ensure that the sample mean is within $16 of the population mean with 95% confidence, we need to find out the sample size that has a probability of 0.95.Probability is given by;P(-1.96 < Z < 1.96) = 0.95The Z-scores are obtained from the standard normal distribution table or calculator. Here, the probability of Z being less than -1.96 is equal to the probability of Z being greater than 1.96. The Z-score for a 95% confidence interval is 1.96. Therefore,1.96 = (289.01 - 273)/σnFor n = 152.94For n = 153, 1.96 = (289.01 - 273)/σ√153The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean.

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The probability density function is defined as the derivative of the cumulative distribution function. It represents the relative likelihood of a continuous random variable taking on a specific value. The total area under the probability density curve is always equal to 1.

For a continuous random variable X, the probability density function f(x) satisfies the following properties:

1. Non-negativity: f(x) ≥ 0 for all x.

2. Integrates to 1: The integral of the probability density function over the entire range of X is equal to 1:

  ∫[−∞, ∞] f(x) dx = 1

This integral represents the total area under the probability density curve, which must be equal to 1.

To calculate the probability of X falling within a certain interval [a, b], we can use the probability density function as follows:

P(a ≤ X ≤ b) = ∫[a, b] f(x) dx

This integral gives the probability that X takes on a value between a and b.

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Answer:

A is No.

B is Yes.

C is Yes.

D is No.

Answer:

Step-by-step explanation:

For A ) yes

B) yes

C) no

D) Yes

Use the formula for mid,

mid(x, y)=((X_1  + X_2)/2,(Y_1+Y_2)/2)

Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

Answer:

Step-by-step explanation:

Candice = 25mph for 4 hours.

Candice has driven= 25 * 4= 100miles.

Liz =50mph

Liz time to catch up to candice= 50 * 2= 100miles.

Therefore, It would have taken Liz two hours to catch up with Candice

The equation represents the line that is perpendicular to the line 5x - 2y =- 6 is y + 4 = -(2/5)(x - 5).

What is the slope-intercept form?

The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Here, we have

The lines of the equations

Ax + By = C1

and Bx - Ay = C2 are perpendicular. Therefore, a line perpendicular to 5x - 2y = -6 must take the standard form  2x + 5y = C.

Substituting x = 5, y = -4, we get  

C = 2(5) + 5(-4) = 10 - 20 = -10.

Thus, 2x + 5y = -10 is the correct choice.

This can be rewritten in slope-intercept form:

2x + 5y = -10

2x + 5y - 2x = -10 - 2x

5y = -2x - 10

5y / 5 = (-2x - 10) /5

y = -(2/5) x - 2

Its point-slope form is

y - y1 = m(x - x1)

y + 4 = -(2/5)(x - 5)

Hence, the equation represents the line that is perpendicular to the line 5x - 2y =- 6 is y + 4 = -(2/5)(x - 5).

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Answer:

At the store every lollipop coasts $2 you have a coupon that will give you $2 off any purchase.  

Step-by-step explanation:

2= the coast for each single lollipop

x= the number of lollipops you buy

-2= the $2 taken off your purchase due to your coupon

The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000

To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\)  that satisfies the condition C(0) = 2000, we need to integrate the given function twice.

First, we integrate C''(x) to find C'(x):

\(C'(x) = ∫ (4x^2 - 3x) dx\)

To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).

\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)

Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):

\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)

To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).

The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.

\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)

Simplifying further, we have:

\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)

Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:

\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)

Since all the terms involving x become zero when x = 0, we have:

K2 = 2000

Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)

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The area of the region enclosed by y = e²ˣ, y = e⁴ˣ and x = 1 is approximately 0.77425 square units.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To sketch the bounded region enclosed by the curves, we first plot the two functions:

y = e²ˣ (in blue)

y = e⁴ˣ (in red)

And the line x = 1 (in green) which is a vertical line passing through x = 1.

We can see that the two functions e²ˣ and e⁴ˣ both increase rapidly as x increases. In fact, e⁴ˣ grows much faster than e²ˣ, so it quickly becomes the larger of the two functions. Additionally, both functions start at y = 1 when x = 0, and they both approach y = 0 as x approaches negative infinity.

To find the bounds of integration, we need to find the points where the two curves intersect. Setting e²ˣ = e⁴ˣ, we have:

e²ˣ = e⁴ˣ

2x = 4x

x = 0

So the two curves intersect at the point (0,1). Since e⁴ˣ grows much faster than e²ˣ, the curve y = e⁴ˣ will always be above the curve y = e²ˣ. Therefore, the region is bounded by the curves y = e²ˣ, y = e⁴ˣ, and the line x = 1.

To find the area of this region, we can integrate with respect to x or y. Since the region is vertically bounded, it makes sense to integrate with respect to x. The limits of integration are x = 0 and x = 1 (the vertical line).

The area A is given by:

A = ∫₀¹ (e⁴ˣ - e²ˣ) dx

= [ 1/4 * e⁴ˣ - 1/2 * e²ˣ ] from 0 to 1

= (1/4 * e⁴ - 1/2 * e²) - (1/2 * 1) + (1/4 * 1)

= 0.77425 (rounded to five decimal places).

Therefore, the area of the region enclosed by y = e²ˣ, y = e⁴ˣ and x = 1 is approximately 0.77425 square units.

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The length of the bisector of the right angle is approximately 3.536.

(a) To find the length of the bisector of the larger acute angle in the triangle with side lengths 3, 4, and 5, we can use the angle bisector theorem. The angle bisector theorem states that in a triangle, the length of the angle bisector of a vertex divides the opposite side into segments proportional to the lengths of the adjacent sides.

Let's denote the sides of the triangle as follows:

Side opposite the larger acute angle = 5

Adjacent side 1 = 3

Adjacent side 2 = 4

According to the angle bisector theorem, the length of the angle bisector of the larger acute angle can be found by multiplying the length of the side opposite the angle by the ratio of the adjacent sides. Let's calculate it:

Length of the bisector of the larger acute angle = (5 * 3) / (3 + 4)

= 15 / 7

≈ 2.143

Therefore, the length of the bisector of the larger acute angle is approximately 2.143.

(b) In a right-angled triangle, the bisector of the right angle is also the hypotenuse divided by √2. In this case, the hypotenuse is the side with length 5. Therefore, the length of the bisector of the right angle is:

Length of the bisector of the right angle = 5 / √2

= 5√2 / 2

≈ 3.536

Therefore, the length of the bisector of the right angle is approximately 3.536.

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