Joan had 382 apples to divide among 33 bags. If she gave an even
amount to each bag, how many will she have left? *
1 point
Your answer
This is a required question

Answer:

r= -1/5

Step-by-step explanation:

Step 1: Remove the parentheses (5r-10= -51)

Step 2: Move the constant to the right-hand side and change the sign (5r= -51 + 50)

Step 3: Calculate the sum of -51 +50 (5r = -1)

Last Step: Divide both sides by the equation by 5 (r = -1/5)

The solution for r in the equation is -1/5

The equation given is 5(r-10)= -51

To solve this question, use the distributive property. The distribute property entails expanding the terms in the bracket. This means multiply the terms in the bracket by 5

5(r - 10)

= 5 x (r - 10)

= 5r - 50

The equation then becomes : 5r - 50 = -51

The second step is to combine similar terms. This would be done by making use of the additive property of equalities: 50 would be added to both sides of the equation

5r = -51 + 50

5r = -1

The third step is to divide both sides of the equation by 5

(5r / 5) = (-1 /5)

r = -1/5

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The value of a₅ is 688. The problem provides us with a recursive formula that relates each term of the sequence to the previous term.

We can use this formula to find the value of any term in the sequence, given the value of the previous term.

The recursive formula is:

aₙ = -3aₙ₋₁ - 2

This formula tells us that to find the value of aₙ, we need to take the previous term aₙ₋₁, multiply it by -3, and then subtract 2.

The problem also provides us with the value of the first term a₁, which is 8. Using the recursive formula, we can find the value of the second term a₂:

a₂ = -3a₁ - 2 = -3(8) - 2 = -26

We can repeat this process to find the value of the third term a₃:

a₃ = -3a₂ - 2 = -3(-26) - 2 = 76

Continuing in this manner, we can find the values of a₄ and a₅:

a₄ = -3a₃ - 2 = -3(76) - 2 = -230

a₅ = -3a₄ - 2 = -3(-230) - 2 = 688

Therefore, the value of a₅ is 688.

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If a₁ = 8 and aₙ = -3aₙ₋₁ - 2, then what is the value of a₅?

Answer:

x = 48.6°

Step-by-step explanation:

see photo for explanation

If the population of bacteria doubles every 24 hours, then the value of k is 0.029.

In the given question;

If the population of bacteria doubles every 24 hours, then we have to find the value of k

Given: Differential equation for the population is dp/dt=kp ; where t = hours.

Apply integration on both sides

dp/dt=kp

dp/p=kdt

∫1/p *dp =∫kdt

Inp=k∫1dt

Inp=kt+c …(i)

Let the population at t=0(i.e. initially) be p(0)

Then from equation (i):

For t=0,p=p(0)

Inp(0)=k(0)+c

Inp(0)=c

Put ‘c’ in equation (i), then:

Inp=kt+ Inp(0)

Inp-Inp(0)=kt

In(p-p(0))=kt

(∴ Since loga-logb=log(a/b))

In(p/p(0))=kt …(ii)

Given the population doubles for every 24 hours

i.e. for t=24 hours, p=2p(0)

∴put the value of t=24 & p=2p(0)

Equation (ii)

In(p/p(0))=kt

In(2p(0)/p(0))=24k

In2=24k

k=In2/24

k=0.69314/24

k=0.02888

k=0.029

The value of ‘k’ is 0.029.

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Answer:

120

Step-by-step explanation:

Remember, always round sample size up, regardless of the decimal part. Answer: To find a 95% CI with a margin of error no more than ±3.5 percentage points, where the true population proportion is around 42%, you must survey at least 764 people. 10×764 = 7640; presumably the electorate is larger than that. So, then 10 × 12 = 120

Answer:

15

Step-by-step explanation:

Answer:15

Step-by-step explanation:

An angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

Vertex, the intersection of two lines, is used to measure angles. Internal angles are created by the sides of geometric shapes like triangles and rectangles.

With the triangles that are presented, prove the angle bisector theorem:

There will be equality in the side ratios.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, an angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

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The obtained limit is identical to the limit that was specified. Therefore, the right answer is option C.

Generally, the equation for the limit  is  mathematically given as

\($\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{4}{n} \sqrt{1+\frac{4 i}{n}}$.\)

The goal is to locate the zone whose area corresponds to the value supplied by the limit.

The definite integral of a function is what is used to compute the area of that function that is underneath its graph.

The limit,

\(\lim _{n \rightarrow \infty} \sum_{i=1}^{n} f(a+i \cdot \Delta x) \Delta x\)

where\($\Delta x=\frac{b-a}{n}$\) and \($x_{i}=a+i \Delta x$\) for the interval $[a, b]$, is equivalent to the integral

\(\int_{a}^{b} f(x) d x .\)

The given limit can also be written as

\(\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \sqrt{1+\left(\frac{4}{n}\right)} i \cdot \frac{4}{n} .\)

In this limit, \($\Delta x=\frac{4}{n}$\). It can be observed that\($f(a+i \Delta x)=\sqrt{1+\left(\frac{4}{n}\right)} i$\) which implies that \($a=1$ and $f(x)=\sqrt{x}$.\)

Solve the \($\Delta x=\frac{b-a}{n}$\)equation for as follows:

\(\begin{aligned}\frac{4}{n} &=\frac{b-1}{n} \\4 &=b-1 \\5 &=b\end{aligned}\)

Therefore, the specified limit may be expressed as an integral as follows:

\(\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \sqrt{1+\left(\frac{4}{n}\right) i} \cdot \frac{4}{n}=\int_{1}^{5} \sqrt{x} d x\)

Therefore, the limit that has been provided designates the area of the graph of "sqrt(x)" on the interval.[1,5]

However, none of the available choices are compatible with this choice. So, consider

\(a=0, f(x)=\sqrt{1+x}$ and $\Delta x=\frac{4}{n}$.\)

Find the value of $b$ as:

\($$\begin{aligned}\frac{4}{n} &=\frac{b-0}{n} \\4 &=b\end{aligned}$$\)

Find the value of x_{i} as:

\(\begin{aligned}&x_{i}=0+\frac{4}{n} i \\&x_{i}=\frac{4}{n} i\end{aligned}\)

$$

Thus, the integral \($\int_{0}^{4} \sqrt{1+x} d x$\) can be expressed using the equation \($\int_{a}^{b} f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} f\left(x_{i}\right) \Delta x$\)

\(\begin{aligned}\int_{0}^{4} \sqrt{1+x} d x &=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \sqrt{1+\frac{4 i}{n} \frac{4}{n}} \\&=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{4}{n} \sqrt{1+\frac{4 i}{n}}\end{aligned}\)

In conclusion, The obtained limit is identical to the limit that was specified. Therefore, the right answer is option C.

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CQ

The complete Question is attached below

Supervisor can choose 6435 different such 8 people committees from 15 call center agents.

We know that we can choose ' r ' number elements or persons from ' n ' number of elements or persons respectively in C(n, r) ways if we do not replace once chosen elements.

Here the total number of staff of call center agent is = 15

So n = 15.

And supervisor of the call center has to choose 8 agents from that group of 15 agents.

So, here r = 8.

Here as supervisor chooses a person he or she cannot be selected as two people.

So the event is without replacement.

Thus by the combination formula, the number of different such committees can be chosen by supervisor is = C(15, 8) = 6435.

Hence, supervisor can choose 6435 different such 8 people committees from 15 call center agents.

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Answer:

n = -8, 7

Step-by-step explanation:

Your equation is:

\(\displaystyle{n^2+n=56}\)

Arrange the terms in the quadratic expression, ax² + bx + c:

\(\displaystyle{n^2+n-56=0}\)

Factor the expression, thus:

\(\displaystyle{\left(n+8\right)\left(n-7\right)=0}\)

This is because 8n-7n = n (middle term) and 8(-7) = -56 (last term). Then solve like a linear which results in:

\(\displaystyle{n=-8,7}\)

Hello!

\(\sf n^2 + n = 56\\\\n^2 + n - 56 = 0\\\\\\n = \dfrac{-b\±\sqrt{b^2-4ac} }{2a} \\\\\\n = \dfrac{-1\±\sqrt{1^2-4*1*(-56)} }{2*1}\\\\\\n = \dfrac{1\±15}{2} \\\\\\\boxed{\sf n = 7 ~or ~-8 }\)

The experimental design that will create probabilities that vary the least from their theoretical probabilities is option B: Flip a coin 5 times and record the number of tails that occur.

When conducting probability experiments, the Law of Large Numbers states that as the number of trials increases, the experimental probabilities will approach the theoretical probabilities more closely. However, this convergence to the theoretical probabilities occurs more rapidly when the number of trials is larger.

In options A, C, and D, the number of coin flips is significantly larger (500, 5000, and 50, respectively) compared to option B, which only involves 5 coin flips. As a result, options A, C, and D are more likely to exhibit greater variation from the theoretical probabilities.

With only 5 coin flips in option B, the outcomes may deviate from the expected probabilities due to the small sample size. However, as the number of flips increases, the experimental probabilities will converge more closely to the theoretical probabilities. Consequently, option B is expected to have probabilities that vary the least from their theoretical values among the given options.

It is worth noting that although option B will have less variation from theoretical probabilities compared to the other options, there may still be some variation due to random chance inherent in the coin flipping process.

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The solution to the system of equations is (15, 30).

A group of two or more equations that must be solved all at once is known as a system of equations. The system's equations each show how two or more variables relate to one another. The variables' values that satisfy every equation in the system can be discovered using algebraic techniques.

Algebraic systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. The substitution approach involves solving one equation for one variable in terms of the other variable, and then substituting the result for that variable's expression into the other equation.

The given system of equations are y=x + 15, y= 2x.

Substitute the value of y from equation 2 in equation 1:

x + 15 = 2x

15 = x

Substitute the value of x to get the value of y:

y = 2x = 2(15) = 30

Hence, the solution to the system of equations is (15, 30).

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Answer:

Step-by-step explanation:

For every 4 boys there are 5 girls and 9 students at the school. So that means that 49 of the students are boys. 49 of the total number of students is 120 students:

49×?=120

If 49 the number of students is 120, then 14 of 120 is 19 of the total number of students. In other words, 14×120=30 is 19 the total number of students. Then 9 times this amount will give the total number of students:

9×30=270

So there is a total of 270 students at the school. Note that this is equivalent to finding the answer to the division problem:

120÷49=?

We can see all of this very succinctly by using a tape diagram:

Bar_diagram_67722d3e6005449e4fbe5c57eaad4f3c

There are 4 units of boys and 9 units of students. Therefore 4/9 of the students are boys.

4 units = 120

1 unit = 30

9 units = 270

There are 270 students altogether.

Students can multiply the numbers in the first row by 10 to get the second row, and then double that amount to get the third row. Adding the entries in the second and third row gives the fourth row that has the solution.

Alternatively, since 120÷4=30, students can just multiply the numbers in the first row by 30 to get the values in the fourth row.

In every row, we can see that the fraction of the students that are boys is 49.

looking at the last row, we can see that the total number of students will be 4×30+5×30=120+150=270.

A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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Based on common factors, Fatoumata can increase each dimension of the deck by 2 feet so that the deck's new area is increased by 50% to 126 ft².

Common factors are the numbers that can divide another number evenly without a remainder.

In this situation, 9 and 14 can divide 126 equally and the product of 9 and 14 are 126.

The old dimensions of the deck:

Width = 7 feet

Length = 12 feet

Area = 84 ft² (7 x 12)

The expected new area of the deck:

Increase in the new area = 5%

Increased factor for the area = 1.5 (100% + 50%)

Area = 126 ft² (84 x 1.5)

The common factors of 126 include 9 and 14 and the product of 9 and 14 = 126.

Therefore, we can increase each length of the deck by 2 feet.

Check:

Width = 9 feet

Length = 14 feet

Area = 126 ft² (9 x 14)

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Answer:

the answer is 9.6 cm

Step-by-step explanation:

.........................

the arc length of the sector is 7.85 meters.

The circumference is define for a circle is given by the formula:

C = 2πr

where C is the circumference, π is the value of pi, and r is the radius of the circle.

In this case, the circumference of the circle is given as 20π meters. So we can write:

20π = 2πr

Dividing both sides by 2π, we get:

r = 10 meters

The arc length of a sector of a circle with central angle θ and radius r is given by the formula:

Arc length = (θ/360°) x 2πr

where θ is the central angle in degrees.

In this case, the central angle of the sector is 45°, and the radius of the circle is 10 meters. So we can substitute these values into the formula:

Arc length = (45/360) x 2π(10) = (1/8) x 20π = 2.5π

Using the value of pi as 3.14, we can calculate the arc length as:

2.5π = 2.5 x 3.14 = 7.85 meters

Therefore, the arc length of the sector is 7.85 meters.

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Answer:

c = 49

Step-by-step explanation:

A perfect square trinomial is of the form (x + a)²

If we expand (x + a)² we get:

x² +  2ax + a²

Compare this to the specific equation given:
x² +   2ax + a²
x²  +   14x + c

Comparing like terms in both equations:
2ax = 14x ==> 2a = 14 ==> a = 14/2 = 7

Therefore a² = 7²

= 49
and this must be the value of c in the equation

Therefore c = 49

Answer:

BE = 39/5 or 7.8

Step-by-step explanation:

As <ABC = <DBE trigonometric function is angle BAC and angle BED

so sin (<ABC) = sin(<DBE) and AC and BC , BD and BE

so AC/AB = DE/BE = 13/BE = 5/3

So now we cross multiply

BE = 13 × 3 over 5

13 × 3 = 39

and over 5 means

39/5 = 7.8

We need to know that when we are adding a negative number, is the same as subtracting that number.

So:

Now, we simply add negative numbers:

Correct option: number 3 = -21

a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).

a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).

Therefore, ln(7x) can be expanded as ln(7) + ln(x).

b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).

Hence, ln(x + 3) remains as it is since we cannot simplify it further.

c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).

Thus, ln(x^8) becomes 8 * ln(x).

d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).

Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].

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If the birth rate were to decline in a population, the growth curve would be affected as well. A decrease in the birth rate would cause the population growth to slow down, resulting in a change in the shape of the curve.

Initially, the exponential curve illustrates slow population growth, followed by a rapid increase over time. However, with a declining birth rate, the curve would likely transition into a logistic growth curve. This type of curve is characterized by an initial period of slow growth, followed by a phase of rapid growth, and eventually leveling off when the population reaches its carrying capacity or other limiting factors come into play.

The projections for the population growth would also be impacted by the decrease in the birth rate. Lower birth rates typically lead to slower growth rates, and in some cases, may even result in a population decline if the birth rate falls below the death rate. This change would be reflected in the updated projections for population growth over time.

In summary, if the birth rate were to decline in a population with an exponential growth curve, the curve would likely shift towards a logistic growth pattern, with slower overall growth and eventual leveling off. The projections for population growth would need to be adjusted to account for the changes caused by the reduced birth rate.

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We can write the volume of the water in the water tank is 9/10 cubic meters.

The volume of a cuboid is given by -

V = Length x Width x Height

V = L x W x H

Given is that a water tank in the shape of a cuboid has length 1.5 meter's and width 1 meter. The water in the tank is 60 centimeters deep.

We can write the volume of the water tank as -

V = Length x Width x Height

V = L x W x H

V = 1.5 x 1 x (60/100)

V = 1.5 x 3/5

V = 3/2 x 3/5

V = 9/10 cubic meters

Therefore, we can write the volume of the water in the water tank is 9/10 cubic meters.

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Answer:

a = 26

a ~ 21.8

Read explanation

Step-by-step explanation:

There are two possibilities;

\(a^{2}+c^{2}=b^{2}\)

Or

\(b^{2}+c^{2}=a^{2}\)

This is because one doesn't know the longest side, and hence there are two possibilities as to what the longest side is.

1. \(a^{2}+c^{2}=b^{2}\)

Substitute in the given values;

\(a^{2}+(10)^{2}=(24)^{2}\)

\(a^{2}+100=576\)

\(a^{2}=476\)

a=\(\sqrt{476}\)

a~21.8

2.\(b^{2}+c^{2}=a^{2}\)

Substitute in the given values;

\((24)^{2}+(10)^{2}=a^{2}\)

\(576+100=a^{2}\)

\(676=a^{2}\)

\(26=a\)

I believe that may be false

Answer:

Step-by-step explanation:

True.

Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.

This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.

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Answer:

Step-by-step explanation:

The maximum volume of paint that can be stored in the cylindrical tank occurs when it is completely filled. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

In this case, the height of the cylindrical tank is 8 feet and the radius is 3 feet. So we can substitute these values into the formula to get:

V = π(3^2)(8)

V = π(9)(8)

V = 72π

Therefore, the maximum volume of paint that can be stored in the tank is 72π cubic feet, which is approximately 226.2 cubic feet if we round to one decimal place.

Answer:

Step-by-step explanation:

J Square Roots and Cube Roots To find the square root of a number, you want to find some number that when multiplied by itself gives you the original number. In other words, to find the square root of 25, you want to find the number that when multiplied by itself gives you 25. The square root of 25, then, is 5. The symbol for square root is equation.

The value of x will be 0 and x = 5. The correct option is A.

The x-intercept is the point at which a line intersects the x-axis, and the y-intercept is the point at which the line intersects the y-axis.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the x-intercept(s) of the function is the quantity of 5x² - 25x.

The value of the x-intercept will be calculated as,

5x² - 25x = 0

5x( x -25) = 0

5x = 0 and x - 5 = 0

x = 0  and x = 5

Therefore, the value of x will be 0 and x = 5. The correct option is A.

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Answer:

it's x = 5

Step-by-step explanation:

got it right on the test.

Answer:

Step-by-step explanation:

Which statements about the relationship between the two triangles below are true? Check all that apply.Mark this and return