Cesar invested a total of $41000 in two accounts. The first account earned 7% after one year. However the second account suffered a 5% loss in the same time. At the end of one year the total amount of money gained was $1670. How much he invested in each account?

Answer:

D

Step-by-step explanation:

none of the above are correct

Answer:

x is equal to -1/3

hope this helps

Answer: I'm pretty sure x = 3

Step-by-step explanation: 3 times 3 = 9. 9 + 15 = 24. And when I solve for x it equals 3.

Answer:

Please help me important question in image

Step-by-step explanation:Please help me important question in image

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Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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Congruent triangles are two triangles with the exact same shape and size.

This means that all of their angles and side lengths are congruent, or equal. In order to determine if two triangles are congruent, we must first make sure that the angles of both triangles are the same.

We can do this by using the Angle-Angle (AA) theorem, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are congruent. The next step is to check that all three side lengths of both triangles are equal.

We can use the Side-Side-Side (SSS) theorem to do this, which states that if all three side lengths of one triangle are equal to the three side lengths of another triangle, then the two triangles are congruent.

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There will be 16 small circular bubbles.

A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a given point remains constant. The radius is the distance between any two points on a circle and the centre.

The area of a circle is given by the formula A = πr², where A is the area and r is the radius.

The area of the large bubble is A = π(8cm)² = 64π cm².

The area of a small bubble is A = π(2cm)² = 4π cm².

Let's assume that the number of small bubbles is n. Then, the total area of the small bubbles is n times the area of a single small bubble:

n(4π) = 4nπ cm²

According to the problem, the area of the large bubble is equal to the sum of the areas of the small bubbles:

64π = 4nπ

Dividing both sides by 4π, we get:

n = 16

Therefore, there are 16 small bubbles.

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Answer:

20 percent

Step-by-step explanation:

7.5 gallons - 6 gallons = 1.5 gallons

\(\frac{1.5}{7.5}\) × 100 = 0.2 × 100 = 20 %

Answer:

20%

Step-by-step explanation:

First, find how much decrease there was: 7.5 - 6 = 1.5

This means the decrease was 1.5/7.5. To convert this to percentage, divide 1.5 by 7.5:

1.5 ÷ 7.5 = 0.20

0.20 = 20% decrease

Answer:

Step-by-step explanation:

A transformation that changes the orientation of a figure but not the orientation of the vertices is called a "reflection."

A reflection is a transformation that flips a figure over a line, called the "line of reflection." The line of reflection can be a line on a coordinate plane, or it can be a line in the space of the figure. The transformed figure, or the image, is a mirror image of the original figure, with respect to the line of reflection. The line of reflection is the perpendicular bisector of the line connecting any two non-adjacent vertices of the figure, then the figure's orientation remains unchanged but it's flipped over that line.

For example, if you reflect a square over its diagonal line, the square will be flipped but its vertices will still be in the same order, so the orientation won't change.

The ratio is 3:4:5.

Cosine by definition, is adjacent divided by hypotenuse, meaning that the value of the hypotenuse is 5. Then, we are given two other sides that are adjacent to angles A and B, which are 4 and 3 respectively.

This means that there are side lengths 3, 4, and 5, meaning that the ratio of the sides are 3:4:5.

Hope this helps.

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Answer:

Degree of freedoms F(4,40)

Step-by-step explanation:

Given:

There is a study which is involving 5 different groups that each contains 9 participants (totally 45)

The objective is to calculate the degree of freedoms

Formula used:

Numerator degree of freedom = k-1

denominator degree of freedom=N-K

Solution:

Numerator degree of freedom = k-1

denominator degree of freedom=N-K

Where,

K= number of groups = 5

N= total number of observations

which is given as follows,

N=45

Then,

Numerator degree of freedom = k-1

=5-1

=4

Denominator degree of freedom = N-K

=45-5

=40

Therefore,

Degree of freedoms, F(4,40)

Using the Linear Pair Postulate, the measure of the angle marked R is calculated as: D. 129°.

The Linear Pair Postulate states that if two angles form a linear pair, their measures add up to 180 degrees. Usually, two adjacent angles on a straight line are a linear  pair, which means they would add up to 180 degrees.

In the image given, we see that angle marked R and 51 degrees are on a straight line, therefore:

m<R = 180 - 51

m<R = 129°

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Answer:

Step-by-step explanation:

abcd=540

2(5)9a=540

90a=540

a=540/90

a=6

Answer:

the digit 3 (or 30,000,000,000) is in the ten billions place.

Answer:

Girl how do you not know this is the most easiest thing /hj

Step-by-step explanation:

its a linear and strong association bc the dots are very refined and stuck together very well

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Down payment = down payment percent times purchase price.

The down payment is computed as down payment Equals down payment % times purchase price. For this computation, the down payment percentage must be converted to a decimal. Divide your annual interest rate by the amount of payments you’ll make. If your interest rate is 6% and you make monthly payments, divide 0.06 by 12 to get 0.005. Multiply that figure by your remaining loan balance to get how much interest you’ll pay that month.

The Excel PMT function is a financial function that computes loan payments based on a fixed interest rate, the number of periods, and the loan amount. The acronym “PMT” refers for “payment” hence the function’s name.

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To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

0.4207149;0.7271136; 0.3063987; 0.04979 ; 0.01832

Step-by-step explanation:

For an exponential distribution:

IF Mean time until failure = 23100

λ = 1/ 23100 = 0.0000432900

What is the probability that a randomly selected fan will last at least 20,000 hours

x ≥ 20000

P(X ≥ 20000) = 1 - P(X ≤ 20000)

1 - P(X ≤ 20000) = [1 - (1 - e^(-λx))]

1 - P(X ≤ 20000) = [1 - (1 - e^(-0.0000432900*20000)

1 - P(X ≤ 20000) = [1 - (1 - 0.4207148)]

1 - P(X ≤ 20000) = 1 - 0.5792851

1 - P(X ≤ 20000) = 0.4207149

11) What is the probability that a randomly selected fan will last at most 30,000 hours?

x ≤ 30000

P(X ≤ 30000) = 1 - e^(-λx)

P(X ≤ 20000) = 1 - e^(-0.0000432900*30000)

= 1 - e^(−1.2987)

= 1 - 0.2728863

= 0.7271136

111) What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?

0.7271136 - 0.4207149 = 0.3063987

B) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?

More than two standard deviation

X = 23100 + 2(23100) = 23100 + 46200 = 69300

Using the online exponential probability calculator :

P(X > 69300) = 0.04979

C) What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?

X = 23100 + 3(23100) = 23100 + 69300 = 92400

P(X > 92400) = 0.01832

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

In linear equation, x = 18 is the value of x in equation .

What is a linear equation example?

6x +4(x - 10) = 140.

6X + 4X - 40 = 140

10X = 140 + 40

10x = 180

  x = 180/10

  x = 18

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The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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Part(A),
The given digits can be used to create 300 even four-digit numerals.

Part(B),

These four-digit numbers come in a set of 60.

A. If the numbers must be even:

The units digit has six options: 2, 4, 6, 8, or 0. The units digit cannot be 1, 3, 5, 7, or 9, as they are all odd numbers.

Use any of the last five digits; for the hundreds digit, use any of the last four digits. The tens digit can be represented by any of the last three digits.

The sum of the digits 1, 3, 5, 7, 8, and 9 yields the following number of even four-digit numbers:

5 × 5 × 4 × 3 = 300

The given digits can be used to create 300 even four-digit numerals.

A. If the sum is less than three thousand:

Four-digit numbers are less than 3000, hence a thousand digits must be 1. There are five possibilities for the units digit (since we cannot use 1 or 3).

With each digit appearing just once or twice, the total number of four-digit numbers that may be made that are fewer than 3000 is:

5 × 4 × 3 = 60

There are 60 such four-digit numbers.

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The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer:

The first step is to label the points being (1,2.3),(6,6.8) in which the first ordered pairs is the number of weeks, and the second one is the dollars in millions.

Hence, the slope is: m=(6.8-2.3)/(6-1) = 4.5/5 = 9/10 = 0.9

The slope represents the dollar rate in the millions per week. In this case, the movie grossed $0.9 million per week from week one to the sixth week.

The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3

We are given the function;

f(x) = 2x² + 3

Now, when we translate a function f(x) downwards, the new function becomes;

g(x) = f(x) - a

where a is the amount of units by which the graph was translated.

Thus for translation of 6 units vertically downwards;

g(x) = 2x² + 3 - 6

g(x) = 2x² - 3

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a) The given function is \($\frac{x^2-2x+2}{(x-1)^2(x+2)}$\). The series of this function is \($\sum_{n=0}^{\infty}(-1)^n(n+1)x^n$\). Therefore, the series is alternating (-1).

b) The sum of the first four nonzero terms of the series is \($-1x^1+2x^2-3x^3+4x^4$.\)

c) The interval of convergence is \((-2, 1)\). This is because the denominator \($(x-1)^2(x+2)$\) has a zero at \($x=-2$\) and a zero at \($x=1$\), and the function is undefined at these two points. Therefore, the interval of convergence is the open interval  \($(-2, 1)$\).

Convergence is the process of two or more different entities coming together and becoming one. In mathematics, it can refer to a sequence converging to a limit, or the process of a function approaching a finite value as the number of trials approaches infinity. In technology, convergence can refer to the combining of different media types into a single medium, such as the combination of audio, video, and text into a multimedia presentation.

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Answer:

The correct option - Figure A

Step-by-step explanation:

The exact question is as follows :

Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

To find - Which box plot shows this data set?

Solution -

Given the data is -

1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3

Firstly,

Arrange the data from smallest to largest

0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7

Now,

Find the median

Median is the middle value - i.e. (15 + 1)/2 = 8th value

So, we get Median = 2

Now,

Find the Quartile -

The first quartile is the median of the data points to the left of the median.

i.e. Median of 0, 0, 0, 0, 0, 1, 1

so, we get

Q1 = 0

The third quartile is the median of the data points to the right of the median.

i.e. Median of 2, 2, 2, 3, 3, 5, 7

so, we get

Q3 = 3

Now,

Compute the min and the max

Minimum value = 0

Maximum value - 7

So,

five number summary is -

0, 0, 2, 3, 7

And we draw the box as follows -

So,

The correct option - Figure A

Recall that to plot a point in the complex plane we have to know its real part and its imaginary part.

The real part of the given number is

and its imaginary part is

Simplifying the above expressions, and rounding to the nearest integer we get that:

Therefore, the point has coordinates (-1,4).

Answer:

Answer:

Center ( -8, 1 )

Radius ( 13 )

Check the picture below to the left, let's use those sides with the law of sines

\(\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(14^o)}{97}=\cfrac{sin(84^o)}{XZ}\implies XZ = \cfrac{97\cdot sin(84^o)}{sin(14^o)}\implies XZ \approx 398.76 \\\\\\ \stackrel{\textit{now using SOH CAH TOA}}{cos(82^o) = \cfrac{XW}{XZ}}\implies XZcos(82^o)=XW \\\\\\ 398.76cos(82^o)\approx XW\implies 55.497\approx XW\implies \stackrel{\textit{rounded up}}{55=XW}\)

The length of XZ will be 398.76 units. Then the length of XW will be 55.5 units.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

In ΔXYZ, ∠X = 82° and ∠Y = 84°. ∠XWZ = 90° and XY = 97.

The third angle of the triangle ΔXYZ is given as,

∠XYZ + ∠XZY + ∠ZXY = 180°

84° + ∠XZY + 82° = 180°

∠XZY + 166° = 180°

∠XZY = 180° - 166°

∠XZY = 14°

By the sine law, we have

XZ / sin 84° = XY / sin 14°

XZ = 97 x sin 84° / sin 14°

XZ = 398.76

Then the length of XW to the nearest integer will be given as,

cos 82° = XW / XZ

XW = 398.76 x cos 82°

XW = 55.4965

XW ≈ 55.5

The length of XZ will be 398.76 units. Then the length of XW will be 55.5 units.

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