A woman invested $15,000 part in 7% stocks and the remainder in 9% bonds. If her yearly yield from both investments is $1,230.00, how much did she invest at each rate?

The cardinality of set A (n(A)) is 3.

The cardinality of set B (n(B)) is 4.

To find the cardinality of a set, we count the number of elements in that set.

For set A, we need to count the number of integers between -6 and -4 (inclusive).

The integers in this range are -6, -5, and -4.

Therefore, the cardinality of set A (n(A)) is 3.

For set B, we simply count the number of elements given in the set. From the given set B = {-29, 20, 28, 29}, we have 4 elements.

Therefore, the cardinality of set B (n(B)) is 4.

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Answer:1920

Step-by-step explanation:800+1120=1920 Formula:

Divide into 2 cubes. 1 cube are equals base times width times height. 8*10*10=800 1 square equals 800. 14*8*10=1120. add 800 and 1120 to get 1920

Answer:

Option (2)

Step-by-step explanation:

From the picture attached,

Angle 1 and angle 2 are the angles made between two lines intersecting each other at a point and a third line is perpendicular to one of them.

Therefore, both the angles are equal in measure.

Rest all the options are not applicable to show the relation between these angles.

Option (2) will be the correct option.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$834.72\\ P=\textit{original amount}\\ r=rate\to 11\%\to \frac{11}{100}\dotfill &0.11\\ t=years\dotfill &1 \end{cases} \\\\\\ 834.72=P[1+(0.11)(1)]\implies 834.72=P(1.11) \\\\\\ \cfrac{834.72}{1.11}=P\implies 752=P\)

Answer:

107

Step-by-step explanation:

3, 7, 11, 15, 19,

23, 27, 31, 35,

39, 43, 47, 51,

55, 59, 63, 67,

71, 75, 79, 83,

87, 91, 95, 99,

103, 107

32nd term is 107

Answer:

x=3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

14+5x=−5(x−8)+4

14+5x=(−5)(x)+(−5)(−8)+4(Distribute)

14+5x=−5x+40+4

5x+14=(−5x)+(40+4)(Combine Like Terms)

5x+14=−5x+44

5x+14=−5x+44

Step 2: Add 5x to both sides.

5x+14+5x=−5x+44+5x

10x+14=44

Step 3: Subtract 14 from both sides.

10x+14−14=44−14

10x=30

Step 4: Divide both sides by 10.

10x/10 = 30/10

Answer:

x=3

Step-by-step explanation:

1. Rearrange terms

2. Distribute

3. Add the numbers

4. Subtract14 from both sides of the equation

5. Simplify

Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

Answer:

rawrhh!!!

Step-by-step explanation:

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

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

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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Answer:

4, 6, 8

Step-by-step explanation:

Let the three consecutive integers be a, b, and c.

So, first, we know that they are three consecutive even integers. In other words:

\(a=2n,b=2n+2,c=2n+4\)

N is any integer, but the 2n ensures that the outcome is even. Since we want to make the subsequent terms also even, we add 2.

We are told that when the first integer (a) is multiplied by the third integer (c), the result is 2 more than 5 times the second integer (b). In other words:

\(ac=2+5b\)

Substitute:

\((2n)(2n+4)=2+5(2n+2)\)

Distribute both sides:

\(4n^2+8n=2+10n+10\)

Add on the right:

\(4n^2+8n=10n+12\)

Subtract 10n and 12:

\(4n^2-2n-12=0\)

Divide everything by 2:

\(2n^2-n-6=0\)

Factor. Find two numbers that when multiplied equals (2)(-6)=-12 and when added equals -1.

3 and -4 works. Thus:

\(2n^2-4n+3n-6=0\\2n(n-2)+3(n-2)=0\)

Combine:

\((2n+3)(n-2)=0\)

Zero Product Property:

\(2n+3=0\text{ or } n-2=0\)

Solve for n:

\(n=-3/2\text{ or } n=2\)

So, n is either -3/2 or 2.

That means that a must be either:

\(a=2(-3/2)\text{ or } 2(2)\)

Multiply:

\(a=-3\text{ or } 4\)

The first answer is not even. So:

\(a=4\)

Our first answer is 4.

And our sequence is 4, 6, and 8.

Checking:

4 times 8 is 32.

2 plus 5 times 6 is also 32.

So our answer is correct.

Answer:

The answer would be -3 1/18

Step-by-step explanation:

Hope this helps :)

Answer:

Is that your answer ☺️☺️☺️. If I'm right so,

Please mark me as brainliest. thanks!!!

The equation of the ellipse is \((x - 3)^2 / 16 + (y - 3)^2 / 64 = 1.\)

To determine the equation of the ellipse, we need to find its major and minor axes, as well as the distance from each focus to the center.

Given that the foci of the ellipse are located at (3, 1) and (3, 5), we can determine that the center of the ellipse is at the midpoint between these two foci, which is (3, 3).

The endpoints of the minor axis are (7, -2) and (-1, -2), which tells us that the length of the minor axis is 7 - (-1) = 8 units.

Now, let's calculate the distance from the center to one of the foci. Using the distance formula, we have:

sqrt((3 - 3)^2 + (3 - 1)^2) = sqrt(0 + 4) = 2.

Since the foci are vertically aligned, the major axis is vertical. Therefore, the length of the major axis is twice the distance from the center to one of the foci, which gives us 2 \(\times\) 2 = 4 units.

Using the standard form of the equation for an ellipse centered at (h, k), with a horizontal major axis of length 2a and a vertical minor axis of length 2b, the equation is:

\((x - 3)^2 / 4^2 + (y - 3)^2 / 8^2 = 1.\)

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Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

Answer:

9: 71 , 10: 110, 11: 52

Step-by-step explanation:

the sum of angles in a triangel is 180°

so for 9:

180 = 78 + 31 + x

180 - 78 - 31 = x = 71

it's a sharp triangel because all angles are smaller than 90°

you can calculate the angles of 10 and 11 the same way

which gives 10: 110°

this is a stump triangel because there s an angle greater than 90°

The last one is a right triangel because it has a 90° angle (marked with the square)

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

Answer:

\(y=\frac{2}{5}x-3\)

or

\(y+3=\frac{2}{5} (x-0)\)

Step-by-step explanation:

We are given two points on Line A: (0,-3) and (5,-1). We can assign each integer to a variable in the slope formula (see above):

\(x_1=0\)

\(y_1=-3\)

\(x_2=5\)

\(y_2=-1\)

As we have identified point, we can now work to identify slope by substituting our points into the slope formula:

\(m=\frac{-1-(-3)}{5-0}=\frac{2}{5}\)

Now that we have identified both point and slope for Line A, we can format these values in point-slope form. Substitute values into the formula:

\(y-(-3)=\frac{2}{5} (x-0)=y+3=\frac{2}{5}x\)

Solve for \(y\) to achieve an answer in slope-intercept form (\(y=mx+b)\):

\(y=\frac{2}{5} x-3\)

Answer:

A

Step-by-step explanation:

40

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

3 students

Step-by-step explanation:

12 - (7 + 2) = 3 students

Given equation is 2x²+x-28 = 0

⇛ 2x²+8x-7x-28 = 0

⇛ 2x(x+4)-7(x+4) = 0

⇛ (x+4)(2x-7) = 0

⇛ x+4 = 0 or 2x-7 = 0

⇛ x = -4 or 2x = 7

⇛x = -4 or x = 7/2.

Answer:

$10.00

Step-by-step explanation:

I would assume there are more ways to do it, but I converted 3/5 into 6/10. $6.00 were spent on 6/10 of a yard of fabric left. From this we can tell that $10.00 is how much a yard would cost because when it is converted into tenths the $6.00 aligns with 6/10 of a yard.

Hopefully that helped I don't know if I explained it very well. :P

The statement fourth "No, the flowers were not put into groups first and then randomly assigned the two additives would be correct.

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a random experiment. To avoid any ambiguity or surprise, a random experiment must be properly defined.

We have:

Total number of flowers selected  = 20

And puts in each vase with same amount of water.

10 flowers have been assigned to receive the new additive.

The remaining 10 flowers receive the original additive.

Based on the data, this is not a randomized block design for the experiment because the flowers were not put into groups first and then randomly assigned the two additives.

Thus, the statement fourth "No, the flowers were not put into groups first and then randomly assigned the two additives would be correct.

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Answer:

Step-by-step explanation: true

Answer:

∅ = 40.3°

General Formulas and Concepts:

Trigonometry

Step-by-step explanation:

Step 1: Define

Looking for m∠A

Step 2: Identify

adjacent leg of ∠A = AC = 7.4

hypotenuse = AB = 9.7

Step 3: Find theta

Step-by-step explanation:6x−2y=18

Solve for

y

.

Tap for fewer steps...

Subtract

6

x

from both sides of the equation.

−

2

y

=

18

−

6

x

Divide each term by

−

2

and simplify.

Tap for more steps...

y

=

−

9

+

3

x

Rewrite in slope-intercept form.

Tap for fewer steps...

The slope-intercept form is

y

=

m

x

+

b

, where

m

is the slope and

b

is the y-intercept.

y

=

m

x

+

b

Reorder

−

9

and

3

x

.

y

=

3

x

−

9

Use the slope-intercept form to find the slope and y-intercept.

Tap for fewer steps...

Find the values of

m

and

b

using the form

y

=

m

x

+

b

.

m

=

3

b

=

−

9

The slope of the line is the value of

m

, and the y-intercept is the value of

b

.

Slope:

3

y-intercept:

−

9

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

Tap for more steps...

x

y

2

−

3

3

0

Graph the line using the slope and the y-intercept, or the points.

Slope:

3

y-intercept:

−

9

x

y

2

−

3

3

0

image of graph

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

How would you describe the difference between the graphs of f(x) = 2x² and g(x) = -2x²: D. g(x) is a reflection of f(x) over the x-axis.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

In this context, we can reasonably infer and logically deduce that a graph of transformed function g(x) = -2x² would be created by applying a reflection over or across the x-axis to the graph of the parent function f(x) = 2x² as shown in the image attached below.

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