A bag is filled with green and blue marbles. There are 43 marbles in the bag. If there are 7 more green
marbles than blue marbles, find the number of green marbles and the number of blue marbles in the bag.
Equation (use x as your variable):
The number of blue marbles is:____
The number of green marbles is:____

Additional reference geometry such as user-created reference planes can be created to reference other planes besides the default top, left and right planes. The given statement is false

Additional reference geometry is a useful tool in CAD software that allows users to create reference planes, axes, and points to assist in the creation of complex models. While the default top, left and right planes are often used as a starting point for reference geometry, users are not limited to these planes. In fact, users can create reference geometry that references any existing plane, axis, or point within the model. This allows for greater flexibility and precision when creating complex models.

In conclusion, it is false that additional reference geometry must reference the default top, left, and right planes. Users can create reference geometry that references any existing plane, axis, or point within the model for greater flexibility and precision.

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The height of the tower is 9.24 feet. That is, the tower is 9.24 feet tall

From the question, we are to determine how tall the tower is

From the given information,

From a distance of 10 feet, the angle of elevation of the tower at a height 5 feet from the ground is 23 degrees.

Let x represent the length of the tower from a point 5 feet from the ground.

Thus,

The height of the tower will 5 + x feet

Now, we will determine x

Using SOH CAH TOA

tan 23° = x / 10

x = 10 × tan 23°

x = 4.24 feet

Height of the tower is 5 + x feet

Therefore,  

Height of the tower = 5 + 4.24 feet

= 9.24 feet

Hence,

The height is 9.24 feet

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Answer:

1st option

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

Here g(x) = \(\sqrt{x+3}\)

The base graph f(x) has been shifted left 3 units

A plan which would give Genesis the lowest monthly payment is: C. The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.

In order to determine the plan which would give Genesis the lowest monthly payment, we would calculate the simple interest earned over each of the time period.

Mathematically, the simple interest earned can be calculated by using this formula:

A = P(1 + rt)

Where:

Substituting the given parameters into the formula, we have;

A = 9000[1 + (0.09 × 3)]

A = 9000[1 + 0.27]

A = 9000 × 1.27

Future value, A = $11,430.

Next, we would calculate the monthly payment over a period of 36 months as follows:

Monthly payment = Future value/Time

Monthly payment = 11,430/36

Monthly payment = $317.50.

Similarly, we would calculate the compound interest earned on the credit card by using this formula:

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

A = 9000[1 + (0.18/12)]⁽¹² ˣ ⁷⁾

A = 9000[1 + 0.015]⁸⁴

A = 9000 × 1.015⁸⁴

A = 9000 × 3.49258954

Future value, A = $31,433.31.

Next, we would calculate the monthly payment over a period of 84 months as follows:

Monthly payment = Future value/Time

Monthly payment = 31,433.31/84

Monthly payment = $372.21.

In this context, we can reasonably infer and logically deduce that the plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan.

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Answer:

C

Step-by-step explanation:

got 100% on exam

Answer:

9 days, 3hrs

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW

Harry goes on a canoe trip with his scout troop.They will canoe a total of 75 miles and want to travel 8 miles each day .How many days will they need to travel the entire distance? Interpret the remainder.

The total distance the travelled is 75 miles

Distance to travel each day is travel 8 miles each day

Then, number if days they will need to travel the entire distance= 75/8

=9.375 days

The remainder is 3, because ( 9×8)=72

75-72=3

And this can be interpreted as 9 days and 3hours

Algebraic expression for the given statement is

\(9t^2 + 3(2+t)\)

Given :

The product of 9 and t squared, increased by 3 times the sum of 2 and t squared

Product means the multiplication

t squared is \(t^2\)

The product of 9 and t squared is written as

\(9 \cdot t^2\\9t^2\)

lets write the expression for 3 times the sum of 2 and t

3 times (2+t)

\(3(2+t)\)

The product of 9 and t squared, increased by 3 times the sum of 2 and t squared .

Algebraic expression is

\(9t^2 + 3(2+t)\)

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The series diverges.

To compute the first four partial sums for the series with nth term an=1/n, we can use the formula for the nth partial sum Sn:

Sn = a1 + a2 + ... + an

In this case, a1 = 1/1, a2 = 1/2, a3 = 1/3, and so on. Therefore:

S1 = 1/1 = 1
S2 = 1/1 + 1/2 = 1.5
S3 = 1/1 + 1/2 + 1/3 ≈ 1.8333
S4 = 1/1 + 1/2 + 1/3 + 1/4 ≈ 2.0833

To determine whether the series converges or diverges, we need to examine the behavior of the sequence of partial sums {Sn}. If the sequence {Sn} converges to a finite limit, then the series converges. If the sequence {Sn} diverges to infinity or negative infinity, then the series diverges.

In this case, we can see that the sequence of partial sums {Sn} is increasing and appears to be approaching infinity as n increases. Therefore, the series diverges.

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Answer:

7

Step-by-step explanation:

-2 x _ = -14

2(7)=14

(-)x(-) = +

-2(7)=-14

The dimensions are;

Length = 7 meters

Width = 5 meters

The area of a rectangle is expressed as;

Area = length × width

From the information given, we have that;

Length = 2w - 3

Area = 65

Substitute the values

65 = (2w - 3)w

expand the bracket

65 = 2w² - 3w

solve the quadratic equation;

2w² + 13w - 10w - 65

Factorize the terms

w(2w + 13) - 5(2w + 13)

w = 5

Substitute the value

Length = 2w - 3 = 2(5) - 3 = 7

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Answer: he would save15,000

Step-by-step explanation:

Answer:

1). g(x) = \(5^{3x}\)

2). g(x) = \(\frac{1}{3}5^{x}\)

3). g(x) = \(3(5)^{x}\)

4). g(x) = \(5^{\frac{1}{3}x}\)

Step-by-step explanation:

Parent function f(x) = \(a^{x}\) when transformed in the form of  \(g(x)=h(a^{\frac{x}{k} })\)

1). If h > 1, function is vertically stretched.

2). If 0 < h < 1, function is vertically compressed.

3). If k > 1, function is horizontally compressed.

4). If 0 < k < 1, function is horizontally stretched.

Parent function of the given functions in the question is f(x) = \(5^{x}\)

g(x)= \(\frac{1}{3}(5^{x})\), parent function is vertically compressed by a factor of \(\frac{1}{3}\).

g(x) = \(5^{3x}\), parent function 'f' is horizontally stretched by a factor of 3.

g(x) = \(5^{\frac{x}{3}}\), parent function 'f' is horizontally compressed by a factor of \(\frac{1}{3}\).

g(x) = \(3(5^{x})\), parent function 'f' is vertically stretched by a factor of 3.

B) m is the independent variable and p is the dependent variable.

Its given in question,

The number of people they will be able to serve depends on the number of meals they prepare. p = the number of people Florence and Anna will be able to serve m = the number of meals Florence and Anna prepare.

Which means people served depends on the meals prepared.

Therefore, p depends on m.

Hence, m is the independent variable and p is the dependent variable.

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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Answer:

Part 1: 10, Part 2: 6

Step-by-step explanation:

The confidence interval is 0.039. This means that the value lies between the range of -0.039 and 0.039. Therefore, we can express the confidence interval as the mean plus or minus the margin of error.

This will give us a range in which the true population mean lies.Let's assume that the mean is 0.259. Then the lower limit of the range is given by:Lower limit = 0.259 - 0.039 = 0.22 And the upper limit of the range is given by:Upper limit = 0.259 + 0.039 = 0.298Therefore, the confidence interval is: 0.22 to 0.298Now we can see that option A is the correct answer: 0.259+0.22.

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Answer:

144°

Step-by-step explanation:

20 hours out of 50 hours is 40%

there are 360° in a circle

so, 40% of 360° is 144°

Each individual result of a probability experiment is called an "outcome" (d).

An outcome refers to a specific result or occurrence that can happen when conducting a probability experiment. It represents the different possibilities or potential results of an experiment.

For example, when flipping a fair coin, the possible outcomes are "heads" or "tails." In this case, "heads" and "tails" are the two distinct outcomes of the experiment.

Similarly, when rolling a fair six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, or 6. Each number represents a different outcome that can occur when rolling the die.

In summary, an outcome is a specific result or occurrence that can happen during a probability experiment. It is essential to understand outcomes as they form the basis for calculating probabilities and analyzing the likelihood of different events occurring.

Thus, each individual result of a probability experiment is called an "outcome" (d).

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The wavelength of the light wave is approximately 729.94 meters.

The speed of light is regarded as a fundamental natural constant. Its relevance extends well beyond its role in characterizing an electromagnetic wave characteristic.

The speed of light is a constant, and it is equal to the product of the frequency of a light wave and its wavelength.

The speed of light is 3 x 108 m/s. If its frequency is 4.11 x 104 Hz

So if the frequency of a light wave is given, we can use this formula to calculate its wavelength:

wavelength = speed of light / frequency

Plugging in the values given in the question, we get:

wavelength = 3 x 10⁸ m/s / 4.11 x 10⁴ Hz

wavelength = 3 x 10⁸/ 4.11 x 10⁴

wavelength = 3 / 4.11 x 10⁸/10⁴

Performing the calculation, we find that the wavelength of the light wave is approximately 729.94 meters.

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a ball of radius 13 has a round hole of radius 3 drilled through its center. then the volume of the resulting solid is 8.5528 x 10³  units³

The radius of the ball is 13 units.

Its volume is

V₁ = (4π*13³)/3

    = 9.2028 x 10³ units³

The drilled hole has the approximate shape of a solid cylinder with radius = 3 and length = 26. Its volume is

V₂ = π*(3²)*26

    = 0.650 x 10³ units³

The volume of the resulting solid is

V₁ - V₂ = 8.5528 x 10³

Answer: 8.5528 x 10³  units³

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Answer:

degree x π/180 = radian

-----------------------------------------

1) -290° × π/180 = -5.061rad

3) 970° × π/180 = 16.93rad

5) 510° × π/180 = 8.901rad

7) 210° × π/180 = 3.665rad

9) 240° × π/180 = 4.189rad

11) -945° × π/180 = -16.49rad

13) 315° × π/180 = 5.498rad

15) -520° × π/180 = -9.076rad

17) 300° × π/180 = 5.236rad

19) 555° × π/180 = 9.687rad

-------------------------------------------

i hope this helps!

Answer: 840 feet squared

Step-by-step explanation:  24ft * 35ft = 840

Yes, it is safe, the chock Carmen used to place behind the wheels of her car.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here

We need to calculate the height of the chock and then compare one-fourth of the height of the wheels to the height of the chock,
So,
The height of the chock is given by Pythagorean theorem,
heigh of chock = √9²- 6²
height of chock = √45
height of chock = 6.71 in

Now,
height of the wheel = 24 in

According to the question, The height of the chocks must be at least one-fourth of the height of the wheels to hold the car securely in place.
height of chock ≥ 1/4(height of the wheel)
6.71 ≥ 1/4(24)
6.71 ≥ 6

Thus, Yes it is safe, the chock carmen used to place behind the wheels of her car.

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Answer:

11.6 i think sorry if i am wrong

Step-by-step explanation:

just do 70 divided by 6 = 11.6

Answer: 420 miles

Step-by-step explanation: 70 miles in 1 hour and then another 70 miles 2 hrs

70+70= 140+70=210+70=280+70=350+70=420

70+70+70+70+70+70= 420

or 70 X 6= 420

To find the week when the farmer should harvest strawberries to maximize their value, we need to use quadratic equations. The equation for the value of strawberries is y = -0.8x^2 + 33x, where y is the value in dollars and x is the number of weeks after the first week of harvesting. To find the maximum value, we need to use the formula x = -b/2a, where a is -0.8 and b is 33. The maximum value occurs at x = 20.625 weeks. Plugging this into the equation, we can find that the maximum value is $527.81. To find the number of bushels that yield the maximum value, we can plug x = 20.625 into the equation for the number of bushels, which is y = 4x + 125. Therefore, the farmer should harvest strawberries in week 21 to maximize their value, and the maximum value is $527.81 for 205 bushels of strawberries.

To solve the problem, we need to use quadratic equations because the value of strawberries decreases linearly each week. The equation for the value of strawberries is y = -0.8x^2 + 33x, where y is the value in dollars and x is the number of weeks after the first week of harvesting. To find the maximum value, we need to use the formula x = -b/2a, where a is -0.8 and b is 33. Plugging these values into the formula, we get x = -33/(2*(-0.8)) = 20.625 weeks. This means that the maximum value occurs at week 21 since we started counting from the first week of harvesting.

To find the maximum value, we need to plug x = 20.625 into the equation for the value of strawberries. Therefore, y = -0.8*(20.625)^2 + 33*(20.625) = $527.81. This is the maximum value of the strawberries.

To find the number of bushels that yield the maximum value, we can plug x = 20.625 into the equation for the number of bushels, which is y = 4x + 125. Therefore, y = 4*(20.625) + 125 = 205 bushels of strawberries.

The farmer should harvest strawberries in week 21 to maximize their value, and the maximum value is $527.81 for 205 bushels of strawberries. The farmer can use this information to plan their harvesting schedule and maximize their profits.

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The equation 2x³ + 2x² - 4x = 0 can be factored as 2x(x + 2)(x - 1) = 0. The solutions are x = 0, x = -2, and x = 1.

To solve the equation 2x³ + 2x² - 4x = 0 by factoring, we first look for the greatest common factor (GCF) of the terms, which in this case is 2x. We can factor it out by dividing each term by 2x:

2x³ / (2x) = x²

2x² / (2x) = x

-4x / (2x) = -2

Now, we have 2x(x² + x - 2) = 0. Next, we factor the quadratic expression (x² + x - 2) into two binomials:

(x + 2)(x - 1)

Therefore, the equation can be factored as 2x(x + 2)(x - 1) = 0. According to the zero-product property, if a product of factors equals zero, then at least one of the factors must be zero.

Setting each factor equal to zero, we find the solutions:

2x = 0    =>    x = 0

x + 2 = 0    =>    x = -2

x - 1 = 0    =>    x = 1

Therefore, the solutions to the equation 2x³ + 2x² - 4x = 0 are x = 0, x = -2, and x = 1. These values satisfy the original equation when substituted back into it. Factoring allows us to find the roots or solutions of a polynomial equation, providing valuable information for solving mathematical problems.

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Answer:

120

Step-by-step explanation:

the angle.of all of these is 180 and 35+25+X=180..

60+X=180...... X=120

The measure of angle D is equivalent to 120 degrees.

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is that the measure of angle B is 25° and the measure of angle C is 35°.

For the triangle, we can write the measure of angle D as -

∠B + ∠C + ∠D = 180°

25° + 35° + ∠D = 180°

∠D = 180° - 60°

∠D = 120°

Therefore, the measure of angle D is equivalent to 120 degrees.

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Answer:

As y = mx + c (standard form)

Thus relating the equation , we get

m = 1

c = -6

Answer:

m = 1

c = -6

Step-by-step explanation:

m is the gradient of the line.

c is the intercept of the line.

The formula for it is : y = mx+c

so m = 1

c = -6

Hope this helps

Answer:

unit

Step-by-step explanation:

proportion are always in same unit

e.g 100m/50m = 1m/2m

Answer:

15

Step-by-step explanation:

Firstly, divide the number of girls by the ratio of girls:

9 ÷ 3 = 3

Now multiply the number of boys in the ratio by 3:

5* 3 = 15

So there are 15 boys.

Hope this helps!

Answer:

15 boys

Step-by-step explanation:

3:5 is your original ratio so..

3*3=9 (girls)

5*3=15(boys)

Also, a small rule to follow with ratios is if for example if you multiply something by 2 then you multiply the other ratio by 2 as well!