A scientist put 14.7 grams of a substance on a scale. She then put another 7.12 grams of the substance on the scale.

How many grams of the substance are on the scale?

The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]

and

[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]

Using the distance formula, we can find the lengths of AP, PB, and AB:

[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]

Substituting these into the section formula, we have:

[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]

Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

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Answer: the team amassed 88i points total, by shooting t two-point baskets and u 1-point free throws.

t+u = 53

total is:  2t + u = 88.

Step-by-step explanation:

hope i makes sense

4 feet.

The length of the rope from the ground to the top of the tent is 4 feet.

To calculate this, subtract the distance from the tent to the ground (2 feet) from the height of the tent (6 feet), and you will get the length of the rope (4 feet).

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Answer:No

Step-by-step explanation:

Because each X is an input, this means that Y is obviously the output.

In order for a set of data, there must ALWAYS be one output for every input, no more, no less. Because this particular set of data has multiple Y values with respect to different X values, this is not a function. Your correct answer is "No, because for each input there is not exactly one output."

Given that the perimeter of the square base is 32 cm, The surface area of the square pyramid is 304 cm².

The surface area of a square pyramid can be calculated using the formula: SA = B + (1/2)Pl, where B is the area of the base, P is the perimeter of the base, l is the slant height, and SA is the total surface area.

Given that the perimeter of the square base is 32 cm, we can divide it by 4 to find the length of each side: 32 cm / 4 = 8 cm.

Now, we can calculate the area of the base by squaring the length of a side: B = (8 cm)² = 64 cm²

Using the given slant height of 15 cm, we can plug in the values into the formula for SA: SA = 64 cm² + (1/2)(32 cm)(15 cm) = 64 cm² + 240 cm² = 304 cm².

Therefore, the surface area of the square pyramid is 304 cm².

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If a research company claims that more than 55% of americans regularly watch public access television, the test statistic for the population proportion is 1.61.

To calculate the test statistic for the population proportion, we first need to set up the null and alternative hypotheses. Let p be the true proportion of Americans who regularly watch public access television.

H0: p ≤ 0.55 (null hypothesis)

Ha: p > 0.55 (alternative hypothesis)

We use a one-tailed test with α = 0.05 level of significance.

Next, we calculate the sample proportion:

p' = 255/425 = 0.60

Then, we calculate the standard error of the proportion:

SE = √(p'(1-p')/n) = √(0.60*0.40/425) ≈ 0.031

Finally, we calculate the test statistic:

z = (p' - p0)/SE = (0.60 - 0.55)/0.031 ≈ 1.61

where p0 is the value of the proportion under the null hypothesis.

The test statistic is approximately 1.61. To determine whether this value provides evidence to reject the null hypothesis, we compare it to the critical value of the z-distribution at α = 0.05 level of significance.

For a one-tailed test with a significance level of 0.05, the critical value is 1.645. Since our test statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to support the claim that more than 55% of Americans regularly watch public access television.

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Photosynthesis is maximum in red light because chlorophyll, the primary pigment responsible for capturing light energy in plants, absorbs red light most efficiently.

What is red light in Photosynthesis?

Red light is a part of the electromagnetic spectrum with a longer wavelength and lower energy than blue and green light.

Red light is particularly effective for photosynthesis because it has a longer wavelength and lower energy, which allows chlorophyll to efficiently absorb it and use it for the photosynthetic process.

In photosynthesis, plants use light energy to synthesize glucose from carbon dioxide and water.

As a result, photosynthesis is maximum in red light because plants can absorb and utilize this light energy most efficiently for their growth and energy production.

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Answer:

The lowest common multiple 3 and 4 is 12.

Step-by-step explanation:

The total multiples of both 3 and 4 between 1 - 100 are 100/12 = 8 4/12 i.e. 8.

the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

To find the interval where both functions F(x) and g(x) are increasing, we need to determine where the derivative of each function is positive. A function is increasing when its derivative is positive, which means that the function is becoming larger as x increases.

The derivative of F(x) can be found by applying the derivative rules for absolute value and addition, which gives us:

F'(x) = 3x/|x|

Now, we need to determine where F'(x) is positive. This occurs when either 3x is positive and |x| is positive, or when 3x is negative and |x| is negative. Therefore, F'(x) is positive for x > 0 and x < 0.

Next, we need to find the derivative of g(x) by applying the derivative rules for subtraction and multiplication, which gives us:

g'(x) = -1 + 8

Simplifying the expression, we get:

g'(x) = 7

Since g'(x) is a constant, it is always positive, which means that g(x) is increasing for all values of x.

To find the interval where both F(x) and g(x) are increasing, we need to identify where both F'(x) and g'(x) are positive. This occurs when x < 0, as this satisfies the condition for F'(x) being positive, and g'(x) is always positive.

Therefore, the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

     <=====o------------------------>

         x<0                    x>0

In this interval, both functions are increasing as x becomes more negative.

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Answer:

no

Step-by-step explanation:

using Pythagorean theorem:

[tex]26^{2} +42^{2}=50^{2}[/tex]

676+1764=2500

2440=2500

2440<2500

Answer:no

To get an output of 5 from a function, the second point must be at a distance of 5 units above the x-axis.

The function represents the relationship between the inputs and the outputs. The function's domain is the set of all possible input values, while the range is the set of all possible output values. The function's graph is the set of all ordered pairs (x, y), where x is the input and y is the output.To get an output of 5 from the function, the second point must be at a distance of 5 units above the x-axis. This implies that the y-value of the second point is 5. The x-value of the second point is arbitrary, and it can be any value. The point (0,5) is an example of a point that is 5 units above the x-axis.

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The probability that the taxi at fault was blue given an eyewitness said it was is approximately 0.436.

To find the probability that the taxi at fault was blue given an eyewitness said it was, we can use Bayes' theorem. Bayes' theorem is expressed as: P(A|B) = (P(B|A) * P(A)) / P(B)

Where:
- P(A|B) is the probability of A given B (the probability the taxi is blue given the eyewitness said it was blue)
- P(B|A) is the probability of B given A (the probability the eyewitness said the taxi was blue given it was actually blue)
- P(A) is the probability of A (the probability the taxi is blue)
- P(B) is the probability of B (the probability the eyewitness said the taxi was blue)

First, let's define our events:
- A: The taxi is blue (Blue Cab), with a probability of 12% (0.12)
- B: The eyewitness said the taxi was blue

Now, we need to find P(B|A) and P(B).

1. P(B|A) = 0.85 (the probability the eyewitness correctly identifies the blue taxi)
2. P(B) can be found using the law of total probability: P(B) = P(B|A) * P(A) + P(B|A') * P(A')
  - A': The taxi is not blue (Green Cab), with a probability of 88% (0.88)
  - P(B|A') = 1 - 0.85 = 0.15 (the probability the eyewitness incorrectly identifies the green taxi as blue)

So, P(B) = 0.85 * 0.12 + 0.15 * 0.88 = 0.102 + 0.132 = 0.234

Now, we can apply Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)
P(A|B) = (0.85 * 0.12) / 0.234
P(A|B) ≈ 0.4359

Rounded to three decimal places, the probability that the taxi at fault was blue given an eyewitness said it was is approximately 0.436 or 436/1000 as a reduced fraction.

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The probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes is 0.33 or 33%.

Uniform distribution is a probability distribution where all outcomes are equally likely. In this case, the time it takes to wash dishes is uniformly distributed between 8 and 17 minutes. This means that any time between 8 and 17 minutes is equally likely to occur.

To find the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes, we need to find the area under the curve of the uniform distribution function between 12 and 15 minutes.

Since the distribution is uniform, the area under the curve between 12 and 15 minutes is simply the width of the interval divided by the total width of the distribution. Mathematically, we can express this as:

P(12 ≤ X ≤ 15) = (15 - 12) / (17 - 8)

P(12 ≤ X ≤ 15) = 3 / 9

P(12 ≤ X ≤ 15) = 0.33 or 33%.

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When the polynomial p(x)=-x^5-2x^3+4x-3, then the value of p(-1) is 3

The Remainder Theorem is a fundamental concept in algebra that relates the value of a polynomial at a certain point to the remainder of the polynomial's division by a linear factor.

The remainder theorem states that when a polynomial p(x) is divided by (x - a), the remainder is equal to p(a).

In this case, we are asked to find p(-1) when p(x) = -x^5 - 2x^3 + 4x - 3.

To use the remainder theorem, we need to divide p(x) by (x - (-1)), which is the same as (x + 1).

We can perform polynomial long division to find the quotient and remainder

The remainder is -x + 2, which means that p(-1) = -(-1) + 2 = 3.

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The Perimeter of the parallelogram whose vertices are given by the coordinates (3 ,6), (-5, 6), (6, -1), (-2, -1) is: 16 + 2√(58)

To find the perimeter of the parallelogram, we need to find the distance between each pair of adjacent vertices and add them up.

First, let's find the distance between (3, 6) and (-5, 6). This is simply the difference between their x-coordinates, which is 3 - (-5) = 8.

Next, let's find the distance between (-5, 6) and (-2, -1). To do this, we need to find the difference between their x-coordinates and their y-coordinates, and then use the Pythagorean theorem. The difference in x-coordinates is -5 - (-2) = -3, and the difference in y-coordinates is 6 - (-1) = 7. So the distance between these two points is √((-3)^2 + 7^2) = √(58).

We can use the same method to find the distance between (6, -1) and (3, 6), which is also √(58).

Finally, we need to find the distance between (6, -1) and (-2, -1), which is simply the difference between their x-coordinates, which is 6 - (-2) = 8.

Adding up all these distances, we get 8 + √(58) + √(58) + 8 = 16 + 2√(58).

So the exact perimeter of the parallelogram is 16 + 2√(58)

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Answer:

a. The triangular prism has 5 faces, 9 vertices, and 12 edges.

b. To find the volume of the packaging, we need to multiply the area of the base (an equilateral triangle) by the height of the prism.

The area of an equilateral triangle with side length 3.6 cm is given by:

$A = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4}(3.6\text{ cm})^2 \approx 5.270\text{ cm}^2$

So, the volume of the Toblerone packaging is:

$V = Ah = (5.270\text{ cm}^2)(21\text{ cm}) \approx 110.59\text{ cm}^3$

Therefore, the volume of the Toblerone packaging is approximately 110.59 cubic centimeters.

Answer:

Y = 4x

Step-by-step explanation:

In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.

The area of the given parallelogram is A- 33(1/2) ft² using the base and height of the parallelogram. the correct answer is (c).

A quadrilateral with two sets of analogous edges is appertained to as a parallelogram. In a parallelogram, the opposing edges are of equal length, and the opposing angles are of equal size. also, the internal angles that are supplementary to the transversal on the same side. 360 ° is the sum of all internal angles. A parallelepiped is a three- dimensional shape with parallelogram- shaped sides. The base( one of the analogous lines) and height( the distance from top to bottom) of the parallelogram determine its area. A parallelogram's border is determined by the lengths of its four edges. The characteristics of a parallelogram are participated by the shapes of a square and cell. What's area? The size of a section on a face is determined by its area. face area refers to the area of an open face or the border of a three- dimensional object, whereas the area of an area area plane region or area  area plane area refers to the area of a shape or planar lamella.

The area of a parallelogram is given by

[tex]base*height.base=8(1/3)ft[/tex]

height=4ft

[tex]Area=b*h =(25/3)*4 =100/3 = 33[/tex]

[tex][base]\frac{1}{3}[(hieght)] ft^{2}[/tex]

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answer - y = -5x + 1

Answer: D = 3c-5

Step-by-step explanation:

The first shape shows the input, C, the second one multiplies it by 3, next, it subtracts C by 5, leaving you with D equaling C times three, minus five.
You can simplify this equation into this:

D=3C (multiplied by 3)

Then subtract by 5
D=3C-5

[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o }{3} \right) +i \sin\left( \cfrac{ 219^o }{3} \right)\right]\implies \boxed{4[\cos(73^o)+i\sin(73^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 579^o }{3} \right) +i \sin\left( \cfrac{ 579^o }{3} \right)\right]\implies \boxed{4[\cos(193^o)+i\sin(193^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=2}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 939^o }{3} \right) +i \sin\left( \cfrac{ 939^o }{3} \right)\right]\implies \boxed{4[\cos(313^o)+i\sin(313^o)]}[/tex]

a. The account balance is $1000 when opened.

b. $1,060 is the balance after 1 year.

c. 42.98 years as per compound interest.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on the accumulated interest from previous periods. This means that interest is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.

In the given question,

a. When the account is opened, t = 0. Therefore, the balance is:

1 × e(0.06 × 0) = 1 × e⁰ = 1

The account balance is $1,000 when it is opened.

b. After 1 year, t = 1. Therefore, the balance is:

1 × e(0.06 × 1) ≈ 1.06

The account balance is approximately $1,060 after 1 year.

c. After 2 years, t = 2. Therefore, the balance is:

1 × e(0.06 × 2) ≈ 1.123

The account balance is approximately $1,123 after 2 years.

Diego's statement is not accurate. The expression In 5 represents the natural logarithm of 5, which is approximately 1.609. It does not represent the time, in years, when the account will have 5 thousand dollars.

To find the time when the account will have a balance of $5,000, we need to solve the equation:

1 × e(0.06t) = 5

Dividing both sides by 1:

e(0.06t) = 5

Taking the natural logarithm of both sides:

ln(e(0.06t)) = ln(5)

0.06t = ln(5)

t = ln(5) / 0.06 ≈ 11.55

Therefore, the account will have a balance of $5,000 after approximately 11.55 years.

We can use the same equation as in part 2 to find out if the account balance will reach $1,000,000. We need to solve the equation:

1 × e(0.06t) = 1000

Dividing both sides by 1:

e(0.06t) = 1000

Taking the natural logarithm of both sides:

ln(e(0.06t)) = ln(1000)

0.06t = ln(1000)

t = ln(1000) / 0.06 ≈ 42.98

Therefore, the account balance will reach $1,000,000 after approximately 42.98 years.

Whether or not this will make you a millionaire by the time you reach retirement depends on when you plan to retire and how much money you need for retirement. If you plan to retire in less than 43 years or you need more than $1,000,000 for retirement, then this account alone will not make you a millionaire.

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To the nearest tenth, the length of each side of the equilateral triangle is roughly [tex]10(\sqrt{(3) - 1)[/tex].

An equilateral triangle has the following three characteristics: identical lengths on all three sides. The three angles are identical. Three symmetry lines may be seen in the figure.

All of the triangle's sides are equal in length since it is equilateral. Call this length "s" for short.

The distance from vertex A to side x, measured in altitude, is equal to the length of side x. Call the intersection of the altitude and side x "P" for short.

The length of AP is [tex](s/2) * \sqrt{}[/tex] because we know that the altitude from vertex A creates a triangle with sides of 30-60-90. (3).

Since side BP is half the length of side AB, we also know that its length is (s/2).

As a result, x's length equals the product of AP and BP:

x = AP + BP

= (s/2) * [tex]\sqrt{(3) + (s/2)[/tex]

= [tex](s/2)(\sqrt{(3) + 1)[/tex]

We are told that x equals 10. We may put the formula we discovered for x equal to 10 and do the following calculation to find s:

[tex](s/2)(\sqrt{(3) + 1)[/tex] = 10

The result of multiplying both sides by two is:

[tex]s(\sqrt{(3) + 1) = 20[/tex]

When you divide both sides by [tex](\sqrt{(3) + 1)[/tex], you get:

[tex]s = 20/(\sqrt{3) + 1)[/tex]

The result of multiplying the numerator and denominator by the conjugate of [tex](\sqrt{(3) + 1), (\sqrt{(3) - 1)[/tex], is as follows:

s = [tex]20(\sqrt{3) - 1)/(3 - 1)[/tex]

= [tex]10(\sqrt{(3) - 1[/tex]

As a result, to the nearest tenth, the length of each side of the equilateral triangle is about [tex]10(\sqrt{(3) - 1[/tex].

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The probability that Mark selects a car key or door key from the key ring is 0.3 or 30%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory provides a framework for understanding random events and the laws of chance, and it is an important tool for modeling and simulating complex systems.

Calculating the probability that he selects a car key or door key :

In this context, we are asked to find the probability of Mark selecting a car key or door key from the key ring. To calculate this probability, we need to first determine the total number of keys on the key ring and then count the number of car keys and door keys.

Total number of keys = 10

Number of car keys = 2

Number of door keys = 1

The probability of selecting a car key or door key can be found by adding the probability of selecting a car key to the probability of selecting a door key. Since there is only one door key and two car keys, the probability of selecting a car key is higher, and we can simplify the calculation by finding the probability of selecting a car key and then adding the probability of selecting a door key that hasn't already been selected.

Probability of selecting a car key = 2/10 = 0.2

Probability of selecting a door key = 1/9 (since one key has already been selected) = 0.1111...

Therefore, the probability of Mark selecting a car key or door key from the key ring is 0.2 + 0.1111... ≈ 0.3 or 30%.

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Yes, this relation is a function and here the domain and range are:

domain = {3,6,2,-7} and range ={0,-2,-1,0}

Domain and Range:

The domain and scope of a function are part of the function. The domain is the set of all input values ​​of a function, and the range is the possible outputs given by the function. Field → Function → Sequence. If there is a function f : A → B such that each element of set A corresponds to an element of set B, then A is the field and B is the codomain. The graph of an element "a" under a relation R is given by "b", where (a,b) ∈ R.

The scope of the function is the set of images. The domain and range of a function are usually expressed as:

Domain(f) = {x ∈ R: State} and range(f)={f(x): x ∈ domain(f)}

According to the Question:

The given function is:

{(3,0),(6,-2),(2,-1),(-7,0)}

It is a function as every input has a single output.

So, 3,6,2,-7 are the elements of the domain of the given relation.

Here domain = {3,6,2,-7} and range ={0,-2,-1,0}

Therefore, this relation is a function.

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The equation that shows how the amount of money Dalton gets in a week, y, depends on the number of times he walks the dog, x is y = 5 + x

Given that

Weekly allowance = $5

Amount earned for walking the dog = $1

The above means that

Total money = Weekly allowance  + Amount earned for walking the dog  * Number of times

So, we have

y = 5 + 1 * x

Evaluate

y = 5 + x

Hence, the equation is y = 5 + x

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the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.

The formula for radioactive decay is given by:

a = [tex]e^(-kt)\\[/tex] * A

where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.

We can use the given information to solve for k as follows:

When t = 0, a = A. So, we have:

A = [tex]e^(0 * k)[/tex] * A

Simplifying this gives:

1 = e^0

Therefore, we can see that k = 0 at the start of the decay process.

Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:

550 = [tex]e^(-8k)[/tex] * 700

Dividing both sides by 700 and taking the natural logarithm of both sides, we get:

ln(550/700) = -8k

Simplifying this gives:

k = ln(700/550)/8

Using a calculator, we can evaluate this expression to get:

k ≈ 0.0445

Therefore, the decay constant for this material is approximately 0.0445.

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