Amber invests $7,000 in bonds and stocks.
• The bonds, b, yield 4% interest annually
• The stocks, s, yield 5% interest annually.
• She earns $320 in income from her investments in a year.
Which of these statements are TRUE about Amber's investments? Select all that apply.

Answer: 16

Step-by-step explanation:

First, calm down.

The area of the trapezoid cannot be found in a straightforward way.

Instead, what we need to do here is divide the trapezoid into two parts, a right triangle and a trapezoid.

Finding the area of the right triangle is easy. You just need to multiply the sides and divide it by 2.

Area of right triangle = 5*4/2 = 10

Next, you need to find the area of the trapezoid.

Area of trapezoid(small) = (2+1)*4/2 = 6

All you need to do now is add the area of these two together, and you get 16.

Answer:

A = 16 units²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the parallel sides b₁ and b₋₂

here h = 4 , b₁ = 6 and b₂ = 2

A = [tex]\frac{1}{2}[/tex] × 4 × (6 + 2) = 2 × 8 = 16 units²

Answer:

2 gallons

Step-by-step explanation:

Make a proportion of gallons of vinegar to batches of salad dressing

[tex]\frac{\frac{2}{5} }{1}[/tex] = [tex]\frac{x}{5}[/tex]

1 x 5 = 5, so

[tex]\frac{2}{5}[/tex] x5  or

[tex]\frac{2}{5}[/tex] x [tex]\frac{5}{1}[/tex] = [tex]\frac{10}{5}[/tex] = 2

The ratio 1/2 is equal to 0.5.To calculate the ratio 1/2, we need to divide 1 by 2. When we divide 1 by 2, we get 0.5. Therefore, the ratio 1/2 is equal to 0.5.

To calculate the ratio 1/2, we need to divide 1 by 2. When we divide 1 by 2, we get 0.5. Therefore, the ratio 1/2 is equal to 0.5.

To calculate the ratio 1/2, we need to divide 1 by 2. This can be done by using a calculator or by hand. When we divide 1 by 2, we get 0.5. This means that the ratio 1/2 is equal to 0.5. In order to calculate the ratio, we can use the formula a/b = c, where a is the first number, b is the second number, and c is the result. In this case, a is 1, b is 2, and c is 0.5. Therefore, the ratio 1/2 is equal to 0.5.

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Answer:

48

Step-by-step explanation:

Rate of change;

20 seconds 30 turns

30/20 is the number of turns per second.

3/2 x 12 = 18  There were 18 turns in the 12 seconds plus the 30 turns that she did in 20 seconds for a total of 18 + 30 = 48 turns

The coordinates of the orthocenter of the triangle J(3,-2) K(5,6) L(9,-2) are (5, -2).

Generally, The orthocenter of a triangle is the intersection of the lines that contain the altitudes of the triangle.

To find the coordinates of the orthocenter, we first need to find the equations of the lines containing the altitudes.

To find the equation of the altitude from vertex J, we need the coordinates of J, K, and L.

Using the given coordinates, we have J(3,-2), K(5,6), and L(9,-2).

The equation of the line containing the altitude from J is:

-2 = (-2-6)/(3-5) (x-5) + 6

The equation of the line containing the altitude from K is:

6 = (-2-6)/(5-9) (x-9) - 2

The equation of the line containing the altitude from L is:

-2 = (6-(-2))/(5-3) (x-3) + 2

Solving the equation of the line containing the altitude from J and L, we get the x-coordinate of the orthocenter is 5 Solving the equation of the line containing the altitude from K and L, we get the y-coordinate of the orthocenter is -2

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The final function after transformations, is [tex]f(x +8) = \sqrt[3]{x+8} - 3[/tex]

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. The modification of algebraic equations is a typical form of algebraic problems. Sometimes graphs are translated, or moved about the xy-plane; sometimes they are stretched, rotated, inverted, or a combination of these transformations.

Now, there are 2 different transformations applied to the function here.

First Transformation:

[tex]f(x) = \sqrt[3]{x}[/tex] is translated 3 units in the negative y direction.

After transformation, the function is [tex]f(x) = \sqrt[3]{x} - 3[/tex].

Second Transformation:

The function [tex]f(x) = \sqrt[3]{x} - 3[/tex] is translated 8 units in the negative x direction.

After transformation, the function is [tex]f(x +8) = \sqrt[3]{x+8} - 3[/tex].

Therefore, the final function, after transformations, is [tex]f(x +8) = \sqrt[3]{x+8} - 3[/tex].

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Answer:

Step-by-step explanation:

To get the answer, you have to do 3·4·3·2=how many are possible.

So the answer is D, 72 possible out comes.

There are 72 ways possible reading assignments.

The fundamental counting principle or basic principle of counting is a method or a rule used to calculate the total number of outcomes when two or more events are occurring together.

Given that, students need to prepare assignments from 4 genres: 3 comedies, 4 mysteries, 3 classics, and 2 poetry.

So, the total possible outcomes = 3 × 4 × 3 × 2 = 72

Hence, there are 72 ways possible reading assignments.

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Answer:

Step-by-step explanation:

As DY is parallel to FS  which is  DJ/FD = JY/SY.

50/x  = 42/63.

1/x = 42/(50 × 63)

x = (50 × 63)/42

x = 3150/42

x = 75 units

Answer:

Step-by-step explanation:

Use proportion- 63/42 as x/50

Use cross multiplication  63 times 50 = 42 times x

3150 = 42x

3150 divided by 42 = 75

The answer is:  x= 75

The value of US$4.50 in Eastern Caribbean currency is 12.15 dollars.

The exchange rate for one United States dollar (US $1.00) is two dollars and seventy cents in Eastern Caribbean currency (EC$2.70) .

Therefore, the value of US$4.50 in EC currency can be computed as follows:

Using the conversion rate,

1 US dollars = 2.70 Eastern Caribbean dollars

4.50 US dollars = ?

cross multiply

Therefore,

value of 4.5 US dollars to EC dollars = 2.7 × 4.50

value of 4.5 US dollars to EC dollars = 12.15 dollars

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Runge Kutta method is used for finding approximate solution of differential equation

The term differential equation in math is defined as method of finding the derivative of a function.

This process is used to find the instantaneous rate of change in function based on one of its variables and the common example is the rate change of displacement with respect to time, called velocity.

Here we have to identify the method that is  is used for finding approximate solution of differential equation

As per the definition of differential equation, here we have know that the best suitable method for the given situation is Runge Kutta method.

Because in this method we have done  provides the approximate value of y for a given point x and it only the first order ODEs can be solved using the Runge Kutta RK4 method.

Therefore, the correct option is (c).

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At the interval of 0 to 4, the ball was thrown up into the air and allowed to bounce until it reached its peak height. Then, the ball began to decrease in height until it eventually came to a halt.

The ball's height increased from 0 to 4 meters as it was thrown up and allowed to bounce. Then, the ball's height decreased from 4 meters until it eventually came to a halt. The ball's height increased from 0 meters to 4 meters as it was thrown up into the air and allowed to bounce. The ball reached its peak height at the interval of 0 to 4 meters and then began to decrease in height until it eventually came to a halt. As the ball bounced, the energy of the ball was converted to different forms such as sound, heat, and kinetic energy. The force of gravity also played a role in the decreasing of the ball's height until it eventually stopped. The height of the ball fluctuated between 0 and 4 meters during the interval of 0 to 4 meters and then decreased until it reached its resting point.

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The function f(x) = 4x/(x-16) has vertical asymptotes at x = 16.

To see this, we can factor the denominator:

f(x) = 4x/(x-16) = 4x/x - 16

As x approaches 16 from the left or right, the denominator x-16 approaches 0, but the numerator 4x does not. This means that the function approaches infinity or negative infinity as x approaches 16, indicating a vertical asymptote at x = 16.

To find the end behavior of the function, we can look at the behavior of the function as x approaches positive or negative infinity. We can see that f(x) = 4x/(x-16)

As x increases without bound, x-16 increases without bound. This means that the denominator becomes larger and larger, making the function approach 0 as x approaches positive infinity.

As x decreases without bound, x-16 decreases without bound as well, this means that the denominator becomes smaller and smaller, making the function approach 0 as x approaches negative infinity.

Therefore, the function has a vertical asymptote at x = 16 and approaches 0 as x approaches positive and negative infinity.

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Answer:

f(x) =. 4x/(x-16)

4x= 0 =>x=

x-16= 0

=>x=16

Asymptotes(x) =16

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Pour factoriser 3x + 6, vous devez trouver deux nombres qui ajoutés donnent 6 et qui multipliés donnent 3x. Les deux nombres sont 3 et 2, donc vous obtiendrez : 3x + 6 = 3(x + 2).

b) En déduire une factorisation pour A : A = 3x + 6 + (x + 2)(6x + 8) = 3(x + 2) + (x + 2)(6x + 8) = (x + 2)(3 + 6x + 8) = (x + 2)(9x + 10).

2)a) Pour factoriser B = x**2 - 4 + (x - 1)(x + 2), vous devez trouver deux nombres qui ajoutés donnent x**2 - 4 et qui multipliés donnent (x - 1)(x + 2). Les deux nombres sont x - 1 et x + 2, donc vous obtiendrez : x**2 - 4 + (x - 1)(x + 2) = (x - 1)(x + 2).

b) Pour factoriser C = x**2 + 4x + (x + 1)(x + 4), vous devez trouver deux nombres qui ajoutés donnent x**2 + 4x et qui multipliés donnent (x + 1)(x + 4). Les deux nombres sont x + 1 et x + 4, donc vous obtiendrez : x**2 + 4x + (x + 1)(x + 4) = (x + 1)(x + 4).

The absolute value inequality for the hearing range of each animal is mod(e - 6008) ≤ 5992 and mod(m - 46000) ≤ 45000, respectively.

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound inequality. This holds true for all absolute value inequalities. You can replace > above with ≥ and < with ≤.

To solve absolute-value inequalities, first, we must drop the absolute-value bars and restate the inequality in one of two ways, depending on the case.

According to the question,

The elephant can hear: 16 ≤ e ≤ 12000

The avg hearing = (12000 + 16)/2 = 6008

Tolerance = 12000 - 6008 = 5992

Therefore, the value absolute value inequality for the hearing of the elephant is mod(e - 6008) ≤ 5992.

Similarly,

The mouse can hear: 1000 ≤ e ≤ 91000

The avg hearing = (12000 + 91000)/2 = 46000

Tolerance = 46000 - 1000 = 45000

Hence, the value absolute value inequality for the hearing of the mouse is mod(m - 46000) ≤ 45000.

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Answer: 2.5 meters long

Step-by-step explanation: if 2 cm turns into 1 m, that means that the scale factor for the number is 1/2. 5 * 1/2 = 2.5. Then just convert the cm into m.

Answer: The wall is actually 2.5 meters tall.

Step-by-step explanation: Given that in the picture the broom is 2cm long and in reality the broom measures 1 meter long, along with the fact that 100cm equals 1 meter, we can calculate that anything in reality will be 50 times greater than in the picture.

From there, simply multiply the height of the wall by 50 in order to get the real-life height of the wall (5cm), which is 2.5 meters tall.

[tex]0.02*50=1[/tex]

[tex]0.05*50=2.5[/tex]

Hope this helps!

Unsurprisingly, the general rule can be applied more broadly than the specific rule, which is the difference between the two. The specific rule is only applicable to dependent events; it applies to both independent and dependent events.

What is the main rule for multiplying?

Multiplication Rule The likelihood that both events A and B will occur if events A and B originate from the same sample space is equal to the probability that A will occur times the probability that B will occur provided that A has already occurred.

What is the rule for multiplying independent events?

The multiplication rule for independent events is the sixth rule of probability. P(A and B) = P(A) * P if A and B are two INDEPENDENT events (B).

                              P(A and B) = P(A) * P(B) is a special multiplication rule that is only applicable when the two occurrences are independent of one another. To put it another way, it only functions if the probability of one occurrence does not change for the other.

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Each twelve-bar cycle in the twelve-bar blues form is referred to as a chorus, as well as the overall chord remains the same. The three sections of a big band are rhythm, reed, and brass.

What Characterizes a Chord as Minor or Major? One small adjustment—the third in a scale—is all that separates a major chord from a minor chord. Three notes from the major scale—the first, third, and fifth—are found in a major chord. The first, lowered third, and flatted fifth chords of a major scale that is named for are the notes that make up a minor chord.

A significant (A). A minor; C#; E. (Am). Major in A-C-E-C (C). C minor, E, G. (Cm). the key of C, and G. (D). D minor in D-F#-A key. significant in D-F-A-E. (E). E minor in E-G#-B key. E - G - B.

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The local school board should reject the null hypothesis since 0.000034 < 0.05.

There is sufficient evidence that the true proportion of households with school-aged children that would support starting the school year a week early is significantly different from the true proportion of households without school-aged children.

All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.

A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.

Thus, The local school board should reject the null hypothesis since 0.000034 < 0.05.

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The profit in 1973 is 5.56 which is estimated by the given linear model.

The regression equation is used to predict or estimate the value of the response (or dependant) variables based on an understanding of the explanatory (or predictor) variables.

Let Y represent the profit (or loss) for a certain company X years after 1970. Based on the data shown, a statistician calculates a linear model

Y = -0.80X + 7.96 ....(i)

Using the above model to estimate the profit in 1973

Substitute the value of X = 3 in the equation (i),

Y = -0.80(3) + 7.96

Y = -2.4 + 7.96

Y = 5.56

This is the profit in 1973.

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Answer:

Step-by-step explanation:

The common ratio that Yui should use in her recursive formula is 1.05. This is because each month's total is 5% greater than the previous month's total, which can be represented as 1 + (0.05) = 1.05.

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

Pythagorean theorem:

According to the Pythagorean theorem, in a right triangle (90 degrees), the square of the hypotenuse equals the sum of the squares of the other two sides. Consider the following triangle ABC where BC2 = AB2 + AC2. where AB is the base, AC is the height (height), and BC is the hypotenuse.

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

The distance between points, P and Q can be evaluated by the Pythagoras theorem as follows;

Distance, PQ = √(20-10)² + (36-12)²

PQ = √(100+576)

PQ = √676

PQ = 26.

Therefore, a point whose distance from both P and Q is exactly 13 is the midpoint of PQ.

Therefore,

x = (20 + 10)/2

x = 15

y = (36 + 12)/2

y = 24.

The coordinate of a point whose distance from both P and Q is exactly 13 is; (15, 24)

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Answer:

  (c)  pr +ps +qr +qs

Step-by-step explanation:

You want to identify an expression that can be factored by grouping.

This method of factoring involves grouping terms that have a common factor, then factoring that out. If the entire expression can be factored by grouping, then the result of this first round of factoring is expressions that also have a common factor.

One expression that can be factored by grouping is ...

  pr +ps +qr +qs

  = p(r +s) +q(r +s) . . . . . . . each pair of terms is factored

Now we notice that the factor (r+s) is common to both terms, so we can factor this further:

  = (p +q)(r +s)

The expression that can be factored by grouping is ...

  pr +ps +qr +qs . . . . choice C

<95141404393>

The probability that at least one person receives exactly one aces in their 52 cards is 4/52= 1/13

We define the following events:

A: person A receives exactly two aces in their five cards.

B: person B receives exactly two aces in their five cards.

C: person C receives exactly two aces in their five cards.

We need to calculate P(A∪B∪C). According to the principle of inclusion and exclusion:

P(A∪B∪C)= P(A)+P(B)+P(C)-P(A∩B)-P(A∩C)-P(B∩C)+P(A∩B∩C)

Total outcomes is equal to  because there 52 cards and we select 5 of them.

The probability of each event is given by:

P(A)=P(B)=P(C)===0.0399

where the possible outcomes are 2 aces and 3 of the other cards.

Then, the intersections of the events mean that one player gets 2 aces and the other gets 2 aces too.

P(A∩B)=P(B∩C)=P(A∩C)==0.0001

Finally,

P(A∩B∩C)=0 because it is not possible that the three events occur at the same time due to there are only 4 aces.

P(A∪B∪C)= 0.0399+0.0399+0.0399-0.0001-0.0001-0.0001+0

P(A∪B∪C)=0.1194

The probability that at least one person receives exactly two aces in their five cards is 0.1194.

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Answer:

a. To find the equation for the median-fit line, we need to first determine the slope (m) and the y-intercept (b) of the line. We can use the following formulas to calculate these values:

m = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)

b = median y - m(median x)

Where n is the number of data points, x is the independent variable (year), y is the dependent variable (number of students learning English), Σ means to sum, and xy represents the product of x and y.

For this dataset, we have 5 data points, so n = 5.

x = 2003, 2004, 2005, 2006, 2007

y = 1.600, 1.599, 1.592, 1.570, 1.560

Σx = 10,015

Σy = 7,966

Σxy = 31,948

Σx^2 = 40,307

m = (531948 - 100157966)/(5*40307 - 10015^2) = -0.007

median x = 2005

median y = 1592

b = 1592 - -0.007 * 2005 = 1597.014

The equation for the median-fit line is:

y = -0.007x + 1597.014

b. To predict the number of students who were learning English in California in 2001, we can substitute 2001 for x in the median-fit line equation:

y = -0.007(2001) + 1597.014 = 1600.087

c. To predict the number of students who were learning English in California in 2010, we can substitute 2010 for x in the median-fit line equation:

y = -0.007(2010) + 1597.014 = 1590.028

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The vertical axis in this graph represents Per Capita Personal Income (PCPI) by State for 2004. The missing value on the vertical axis represented by [?] is $38,400.

$38,400

The vertical axis in this graph represents Per Capita Personal Income (PCPI) by State for 2004. The number given to us is $52,000, and the other number given is $20,000. To determine the missing value, we need to calculate the difference between the two numbers. We do this by subtracting $20,000 from $52,000.

$52,000 - $20,000 = $32,000

To find the missing value, we need to add the difference to the given value of $20,000.

$20,000 + $32,000 = $52,000

Therefore, the missing value on the vertical axis represented by [?] is $38,400.

The missing value on the vertical axis represented by [?] is $38,400.

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The car consumes 3 gallons and 8.2 gallons of fuel respectively.

Milage:

Divide the distance traveled by the amount of gas used. For example, driving 100 miles with a full tank and 5 gallons of gas is 10mpg. When it comes to fuel economy, it's important to know how much your car is costing you each time we drive it.

According to the Question:

The gas mileage is the number of miles that can be covered by a car for a particular amount of fuel.

We are given that the gas mileage of the car is 30 miles per gallon, that means that the car consumes 1 gallon of fuel for each 30 miles covered.

The amount of fuel needed to cover the following distance is:

a) For 90 miles, let x represent the number of gallon of fuel. Hence:

Distance covered / amount of fuel = 30 miles per gallon

  90/x = 30

⇒ x = 90/30

⇒ x = 3 gallons

b) For 246 miles, let x represent the number of gallon of fuel. Hence:

Distance covered / amount of fuel = 30 miles per gallon

⇒ 246/x = 30

⇒ x = 246/30

⇒ x = 8.2 gallons

Therefore, the car consumes 3 gallons of fuel for 90 miles and 8.2 gallons for 246 miles.

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As per the permutation method, there are 215,160 different ways are available for making the letters with vowel as the starting letter and s as the ending letter.

The term permutation in math is defined as  a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters

Here we need to find the number of combination for the word that start with a vowel and end with an s.

As we all know that there are 26 letters in alphabets.

so that would be all four letter words - four letter words with no vowel.

Then it can be calculated as the total number of four letter words

=> 26P4 or 26C4*4!

Then the number of four letter words without a vowel is calculated as

=> 21P4

Therefore, it can be written as,

=> 26P4 - 21P4

Then the resulting word count is calculated as,

=> (26 x 25 x 24 x 23) - (21 x 20 x 19 x 18)

=> 215160

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Answer:

11 hours

Step-by-step explanation:

First we divide 335 by 5 to get the hourly rate.

We get 67 as the answer.

Next we divide 737 by 67 and we get 11 hours.

Hope this helps. :)

Answer:

This is an expression. To simplify it, we will combine like terms.

9d - 4p - 6 - 10d + 8 = (-9d - 10d) - 4p - 6 + 8 = -19d - 4p + 2

So the simplified expression is -19d - 4p + 2