There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of exactly 1 red?

Answer:

Yes, Sophia is correct

Step-by-step explanation:

The expression is correct and if you solve it, you get 23 which should be her uncle's age.

Answer:

$1.06

Step-by-step explanation:

5x10=50 or .50

50x2=100 or $1.00

3x2=6 or .06

1.00+.06=1.06

Hope this helps you!!

Answer:

Step-by-step explanation:

v=3+1.5x7

v= 13.5 m/s

9514 1404 393

Answer:

Step-by-step explanation:

The vertex form of the quadratic equation is ...

  y = a(x -h)² +k . . . . . . . . . vertex (h, k); vertical scale factor 'a'

Given the vertex, we can find the scale factor by substituting the given point values:

  11 = a(-1 -3)² -5

  11 = 16a -5

  a = (11 +5)/16 = 1

So, the vertex form equation is ...

  y = (x -3)² -5 . . . . . vertex form

Expanding this gives the standard form.

  y = x² -6x +9 -5

  y = x² -6x +4 . . . . . standard form

Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Work Shown:

Multiply the first coefficient (6) and the last term (-7) to get -42. We need to find factors of -42 that add to -19

Turns out that those two numbers are -21 and 2, which you find by trial and error.

-21 * 2 = -42

-21 + 2 = -19

Break up -19x as -21x+2x and use the factor by grouping method

6x^2 - 19x - 7

6x^2 - 21x + 2x - 7

(6x^2 - 21x) + (2x - 7)

3x(2x - 7) + 1(2x - 7)

(3x+1)(2x-7)

The factorization represents the length*width, since this product is equal to the rectangle's area.

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

Plug x = 15 into each factor

3x+1 = 3*15+1 = 46

2x-7 = 2*15-7 = 23

The length and width are 46 and 23

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Answer:

a. SOLVED

b. \(4c+3b=720\)

c. (Below)

d. 160

Step-by-step explanation:

1 cherry = $4

1 blueberry = $3

60 cherry basket:

60 × 4

= 240

Goal amount = $720

Bw day selling blueberry basket

Money:

= 720 - 240

= 480

Blueberry basket = 480 ÷ 3

\(\frac{480}{3}\)

\(=160\)

Cherry = 60

Blueberry = 160

Answer:

please include the amount of Isaac's purchase and coupon amount.

Step-by-step explanation:

Depending on Isaac's purchase amount, you *.12 to it. That will give you the amount of the commission before the coupon.

Answer:

5 units.

Explanation:

To find the distance between two points in the coordinate plane, use the distance formula below:

Substituting the points gives:

The distance from A to B ​is 5 units.

Answer: The line connecting the point and the line is perpendicular to the original line.

Step-by-step explanation:

(Forgot the name but there is also a theorem stating that the shortest distance between a point and a line is the one that is perpendicular)

The quotient using compatible numbers for 2252 divided by 7 is 321 remainder 5.

Compatible numbers are those that are simple to mentally add, subtract, multiply, or divide. Compatible numbers are close in value to the actual numbers, making it easy to estimate the answer and solve problems.

The following steps are required:

Step 1: Take the dividend's first digit from the left.

Step 2: Next, divide it by the divisor and write the result as the quotient on top.

Step 3: Subtract the result from the digit and record the difference.

Step 4: Subtract the dividend's next digit (if present).

Step 5: Write the value gotten.

A quotient is a quantity created by the division of two numbers in mathematics. The quotient is widely used in mathematics and is also known as the integer component of a division, a fraction, or a ratio. In this case, the value gotten after the division is 321 remainder 5.

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Step-by-step explanation:

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

I think this should help ya! -Furreto

a) The parameter of interest is the mean weight of loaves of bread produced at the bakery. b) The evidence is the sample mean weight of the bread loaves is less than 1 pound.  c) If the P-value is less than or equal to the significance level, we would reject the null hypothesis

What is the P-value?

The P-value means the probability, for a given statistical model that, when the null hypothesis is true, the statistical summary would be equal to or more extreme than the actual observed results.

a. The parameter of interest is the mean weight of loaves of bread produced at the bakery.

The null hypothesis is that the mean weight is equal to 1 pound, and the alternative hypothesis is that the mean weight is less than 1 pound. We can express these hypotheses as follows:

H0: μ = 1

Ha: μ < 1

b. There is some evidence for the alternative hypothesis because the sample mean weight of the bread loaves is less than 1 pound.

If the null hypothesis were true (i.e., the true mean weight is 1 pound), we would expect the sample mean to be close to 1 pound.

The fact that it is less than 1 pound suggests that the new employees may be producing loaves that are too light.

c. The P-value for the test in part (a) is not given, so we cannot interpret it. However, if the P-value were given and it was less than the significance level (e.g., 0.05), we would interpret it as the probability of observing a sample mean at least as extreme as the one we obtained, assuming that the null hypothesis is true.

d. To make a conclusion at the significance level (e.g., 0.05), we would compare the P-value (if given) to the significance level.

If the P-value is less than or equal to the significance level, we would reject the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean weight of the bread loaves is less than 1 pound.

If the P-value is greater than the significance level, we would fail to reject the null hypothesis and conclude that we do not have enough evidence to suggest that the true mean weight is less than 1 pound.

Hence, a) The parameter of interest is the mean weight of loaves of bread produced at the bakery. b) The evidence is the sample mean weight of the bread loaves is less than 1 pound.  c) If the P-value is less than or equal to the significance level, we would reject the null hypothesis.

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Step-by-step explanation:

Let an angle = x

x= 70+(90-x)

x= 160-x

2x=160

x=80

So angle is 80 and it's complementary angle would be 10

Answer:

55∘ and 125∘

Step-by-step explanation:

Supplementary angles sum to

180∘

let one angle be \(x\)

then the other angle is \(x+70\)

summing the 2 angles gives

\(x+x+7=180\)

\(2x+70=180\)

subtract 70 from both sides

\(2x=180 -70=110\)

divide both sides by

\(2x=\frac{110}{2} =55\)

thus the angles are

55∘ and  55 + 70= 125∘

Answer:

no

Step-by-step explanation:

there are somethings you need to know. The given height is the combined height of the cylinder and hemisphere. but we need to use the height of cylinder in the formula so we subtract the original height by radius.

Next thing is that the formula 2πrh is for C.S.A of the cylinder but we need the base area as well for surface area of this combined solid. So we add base area (i.e πr²) to 2πrh.

Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

The solution to the compound inequality given as -3 < -(w + 3) + 4w or -3 >= -3(w - 5) + 6w is w > -2 or w >= -6

The compound inequality is given as:

-3<-(w+3)+4w or -3>=-3(w-5)+6w

Rewrite the compound inequality properly as follows

-3 < -(w + 3) + 4w or -3 >= -3(w - 5) + 6w

Open the brackets in the above compound inequality expression

-3 < -w + 3 + 4w or -3 >= -3w + 15 + 6w

Evaluate the like terms in the above compound inequality expression

-6 < 3w or -18 >= 3w

Divide both sides of the above compound inequality expression by the coefficient of the variable terms

-2 < w or -6 >= w

Rewrite the inequality as:

w > -2 or w >= -6

Hence, the solution to the compound inequality given as -3 < -(w + 3) + 4w or -3 >= -3(w - 5) + 6w is w > -2 or w >= -6

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The length of the arc KL in the given circle is 3.49 units

In a circle whose radius is R, the length of an arc defined by an angle x is given by:

Length = (x/360)*2*3.14*R

Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:

Length = (100/360)*2*3.14*2

Lenght = 3.49 units.

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the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

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Answer:

30n+49/5

Step-by-step explanation:

Answer:

12.8+6(n-0.5)

Putting the value of n into the equation

12.8+6(3.7-0.5)

12.8+6(3.2)

12.8+19.2

32.0

The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

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

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

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The class width of the histogram is 5

A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width called the class width.

The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most common type of histogram.

The class width is plotted in the x - direction. this is the difference between the two consecutive values in the boundary.

class width = 100.5 - 95.5 = 5

class width = 85.5 - 80.5 = 5

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Answer:

542.5

Step-by-step explanation: tRUST ME ON THIS

The total distance in miles that Benjamin travelled during the given time will be equal to 537.5 miles. Hence, option J is correct.

The overall distance the object covers in a given amount of time is its average speed. The scalar quantity represents the average speed. It does not have direction; it is represented by magnitude.

Average Speed= \(Total\ distance/Total\ time\)

As per the given information in the question,

Their average speed of Benjamin is 65 miles per hour for 4.5 hours, then he travels at an average speed of 70 miles per hour for 3.5 hours.

Then the total distance traveled by him will be,

\(Average\ Speed(s)= \frac{Total\ distance(d)}{Total\ Time(t)}\)

d = s × t

d₁ = 65 × 4.5

d₁ = 292.5 miles.

d₂ = s × t

d₂ = 70 × 3.5

d₂ = 245 miles

Then, the total distance (D) will be,

D = d₁ + d₂

D = 292.5 + 245

D = 537.5 miles.

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Answer:

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

Steps should be self-explanatory. Happy to explain if anything is not clear.

Answer:

Step-by-step explanation:

1) 4v + 7 = 7, for v?

→ 4v + 7 = 7

→ 4v = 7 - 7

→ v = 0/4

→ [ v = 0 ]

2) 3(u + 4) = 27, for u?

→ 3(u + 4) = 27

→ 3u + 12 = 27

→ 3u = 27 - 12

→ u = 15/3

→ [ u = 5 ]

3) -20 = 10(h + 5), for h?

→ -20 = 10(h + 5)

→ 10h + 50 = -20

→ 10h = -20 - 50

→ h = -70/10

→ [ h = -7 ]

4) -10 = (n - 52)/5, for n?

→ -10 = (n - 52)/5

→ n - 52 = -10 × 5

→ n = -50 + 52

→ [ n = 2 ]

5) (48/x) - 3 = 3, for x?

→ (48/x) - 3 = 3

→ 48/x = 3 + 3

→ 6x = 48

→ x = 48/6

→ [ x = 8 ]

6) 8r = 2r + 42, for r?

→ 8r = 2r + 42

→ 8r - 2r = 42

→ r = 42/6

→ [ r = 7 ]

These are required values.

Answer: 6b^3 (b+3)

Step-by-step explanation:

6b^4+3b^3+15b^3  

3b^3(2b+1+5)    

3b^3(2b+6)

3b^3.2(b+3)        

6b^3(b+3)