Help please

A bank loaned out $25,000, part of it at the rate of 3% annual interest, and the rest at 9% annual interest. The total interest earned for both loans was $1,770.00. How much was loaned at each rate?


$----------- was loaned at 3% and

$-----------was loaned at 9%.

Answer:

one soulution

Step-by-step explanation:

you have 5x 2x and 3x subtract 5 by 3 get 2 divide u get 1 I am not certain but it's an attempt

The answer of the given question based on the scatterplot for determining  when she will reach 10,000 songs the answer is Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

Slope is  measure of  steepness or incline of  line. In geometry and mathematics, slope is defined as  ratio of the change in  y-coordinates to  change in  x-coordinates between two distinct points on  line. This is often represented by  letter "m".

To determine when Maria will reach 10,000 songs, we need to find the point on the line of best fit where the y-value is 10,000.

From the scatterplot, we can estimate that the line of best fit intersects the y-axis at approximately 2000. This means that the initial number of songs downloaded was 2000.

Next, we need to find the slope of the line of best fit. Let's choose the points (5, 6500) and (10, 9500).

The slope of the line passing through these two points is:

slope = (y2 - y1)/(x2 - x1) = (9500 - 6500)/(10 - 5) = 600 songs per month

This means that Maria is downloading 600 songs per month on average.

Finally, we can use the slope-intercept form of a line to find the x-value when the y-value is 10,000:

y = mx + b

10,000 = 600x + 2000

8000 = 600x

x = 13.33

Therefore, Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.

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Answer:

    \(\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1\)

Step-by-step explanation:

Slope intercept form of a line equation is

y = mx + b

where

m = slope

b = y-intercept

A perpendicular line to y = mx + b will have a slope of -1/m

Let's first find the equation for line z in slope-intercept form
Slope m for a line  = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line

Slope of line z is
\(m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}\)

So line z will have an equation of the form
\(y = -\dfrac{3}{5}x + b\)

We know that a line perpendicular to this line will have a slope of
\(- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}\)

So the equation of the perpendicular line is
\(y = \dfrac{5}{3}x + b\)

Only one of the 4 choices, name choice A has this slope of 5/3

Therefore the correct answer choice is A

There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:

The perpendicular line passes through (3, 6). This means when x = 3, y =6

Substitute these values of x, y into the equation for the perpendicular line and solve for b

\(y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1\)

This corresponds to Choice A

Therefore , the solution of the given problem of trigonometry comes out to be using the formula 8 cos³ a - 6 cos a - 1.

According to some, the growth of astrophysics was aided by the blending of various disciplines. Many metric problems may be solved or the results of a computation may be ascertained with the help of precise mathematical techniques. Trigonometry is the study of all six basic geometric computations. They go by a variety of titles and acronyms, including sine, variation, angle, and others. (csc).

Here,

To determine cos 2a in terms of cos a, we can use the double angle cosine formula as follows:

=> cos 2a = 2 cos² a - 1

Given that 2 cos 3 = cos a, we can reformat this as follows:

=> cos 3α = (1/2) cos a

Now, we can express cos 3 in terms of cos using the triple angle formula for cosine:

=>  cos 3α = 4 cos³ α - 3 cos α

=>  4 cos³ α - 3 cos α = (1/2) cos a

=>  8 cos³ α - 6 cos α = cos a

=>  cos 2α = 2 cos² α - 1

=>  cos 2α = 2 (cos² α - 1/2)

=>  cos 2α = 2 [(8 cos α - 6 cos α)/2 - 1/2]

=> cos 2α = 8 cos³ α - 6 cos α - 1

As a result, cos 2a can be calculated using the formula 8 cos³ a - 6 cos a - 1.

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Answer:

25 lawns

Step-by-step explanation:

To do this:

first create a ratio

5 L: 8 H

? L : 40 H

Then solve:

you can do this two ways

1. cross multiply

40*5=8?

200/8 = 25

2. divide

40/8 = 5

5*5 = 25

Hope this helps:)

Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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Answer:

câu này là 500 nhen

The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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Answer:

180

Step-by-step explanation:

The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:

A=10×18

A=180

The area of the parallelogram is 180 square units

Answer:

Probability isn't my strong subject, so please review carefully.

Step-by-step explanation:

The possible numbers:

Number  Count    Probability    Chance

    1              2               2/5           40%

    3              1               1/5             20%

    5             2               2/5            40%

Sum             5                  1             100% [chance you'll get any number]

The probability of getting the number 1 is 2/5 or 40% on the first draw.  The probability of getting 6 1's in 10 draws is:

\((2/5)^{10}\) = 0.0001049

Try it to determine the experimental probability.  After 10,000 tries you should have at least one success.

Answer:

1184

Step-by-step explanation:

the triangles: 12+10+10 =32.
So the lateral area is 32*34

Then add the 2 triangles areas =2*1/2 *12*8 =96

So add together 32*34+96=1184

Answer:

80%

Step-by-step explanation:

A percentage can also be represented as a fraction with the denominator of 100. If 80 out of 100 (Fraction Form: \(\frac{80}{100}\)), then 80% of the art club members voted.

The lengths of the segments x and y in the right triangles are x = 6√2 and y = 12√2

The given shape is the right-angled triangle

Such that

We have angles = 30 degrees and 45 degrees

The measure of y can be calculated using the following sine ratio

sin(45) = y/24

Make y the subject

So, we have

y = 24 * sin(45)

When evaluated, we have

y = 12√2

The length x is calculated as

sin(30) = x/y

So, we have

x = y * sin(30)

This gives

x = 12√2 * 1/2

Evaluate

x = 6√2

Hence, the value of x in the triangle is 6√2

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Answer:

The point estimate that should be used in constructing the confidence interval is 3.5.

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

American students:

Sample of 12, mean height of 68.4 inches with a standard deviation of 1.64 inches. This means that:

\(\mu_A = 68.4\)

\(s_A = \frac{1.64}{\sqrt{12}} = 0.4743\)

Non-American students:

Sample of 17, mean height of 64.9 inches with a standard deviation of 1.75 inches. This means that:

\(\mu_N = 64.9\)

\(s_N = \frac{1.75}{\sqrt{17}} = 0.4244\)

Distribution of the difference:

\(\mu = \mu_A - \mu_N = 68.4 - 64.9 = 3.5\)

\(s = \sqrt{s_A^2+s_N^2} = \sqrt{0.4743^2 + 0.4244^2} = 0.6365\)

The point estimate that should be used in constructing the confidence interval is 3.5.

Confidence interval:

\(\mu \pm zs\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).  

The lower bound of the interval is:

\(\mu - zs = 3.5 - 1.96*0.6365 = 2.25\)

The upper bound of the interval is:

\(\mu + zs = 3.5 + 1.96*0.6365 = 4.75\)

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

Answer:

\(m_{perpendicular}\) = 6

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 )

given

x + 6y = - 24 ( subtract x from both sides )

6y = - x - 24 ( divide through by 6 )

y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form

with slope m = - \(\frac{1}{6}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6

Answer:

Step-by-step explanation:

There were approximately 6056 no votes.

Let's assume the number of yes votes is represented by the variable "5x," where x is a positive constant.

Similarly, the number of no votes can be represented by "8x" since the ratio of yes votes to no votes is 5 to 8.

The total number of votes is given as 9854, so we can set up the following equation:

\(5x + 8x = 9854\)

Combining like terms, we have:

\(13x = 9854\)

To solve for x, we divide both sides of the equation by 13:

\(x = \frac{9854 }{13}\)

\(x \approx 757.23\)

Since x represents a positive constant, we round it to the nearest whole number, giving us x = 757.

Now, we can find the number of no votes by multiplying x by the ratio of no votes:

No votes \(= 8x\)

\(= 8 \times 757\)

\(= 6056\)

Therefore, there were approximately 6056 no votes.

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The guests in the birthday party ate 33 cookies.

We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.

Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.

6 1/4 dozen = 25/4 dozen

3 1/2 dozen = 14/4 dozen

Now we can subtract the number of cookies that were left from the number of cookies that were made:

25/4 - 14/4 = 11/4 dozen

To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.

There are 12 cookies in one dozen, so:

11/4 x 12 = 33

Therefore, the guests ate 33 cookies.

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Let:

Mp = Marked price = $310

r = Rate of discount = 20% = 0.2

D = Discount

Sp = Sale price

The discount will be given by:

And the sale price will be:

Answer:

a) 0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b) 0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c) 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter.

This means that \(\mu = 65, \sigma = 7.7\)

a. What is the probability that the amount of collagen is greater than 60 grams per.

This is 1 subtracted by the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 65}{7.7}\)

\(Z = -0.65\)

\(Z = -0.65\) has a pvalue of 0.2578

0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b. What is the probability that the amount of collagen is less than 90 grams per.

This is the pvalue of Z when X = 90.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{90 - 65}{7.7}\)

\(Z = 3.25\)

\(Z = 3.25\) has a pvalue of 0.9994

0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?

Between Z = 1 and Z = -1, so the proportion is the pvalue of Z = 1 subtracted by the pvalue of Z = -1

Z = 1 has a pvalue of 0.8413

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826*100% = 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

On solving the provided question, we can say that -  here in graph we have on solving equation  \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

\(2x^2+ 9y^2 \\\)

\(8 + 9 = 17\)

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Answer:

5/16

Step-by-step explanation:

This is a geometric sequence

aₙ=a₁*rⁿ⁻¹

a₆=10*.5⁶⁻¹

a₆=10*.5⁵

a₆=10*(1/2)⁻⁵

a₆=10*1/32

a₆=10/32=5/16

The following steps would apply conditional formatting to the range:

The given parameters in the question are:

The Conditional Formatting is located on the home tab

So, the first step to select the range and locate the Conditional Formatting option

Then set the necessary conditions and formats

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Answer:

297 sq ft

Step-by-step explanation:

the width is 9 and the length is 33

9x33=297

Answer: C, F

Step-by-step explanation: this is a form of distribution meaning you have to distribute -10 to the numbers inside the parenthesis. -10x4= -40x and -10 x -5= 50 therefor it is -40x+50. This answer can work as commutative meaning -40x+50 can also be written as 50-40x

Answer:

8/4 + 4/4

Step-by-step explanation:

Try it im not good at math :( but hope it helps :(:

Answer:

14 & 21

Step-by-step explanation:

14 + 21 = 35

21 - 14 = 7

Answer:

21 & 14

Step-by-Step explanation:

35 minus 7= 28 then divide that by 2 and you get 14 so now add the 7 to 14 and you get 21 and that will be the bigger number.

Answer:

w² - 2w + 4

Step-by-step explanation:

(w² - 4w + 14) - (2w + 10) = w² - 2w + 4

To construct a line segment that is half the length of segment AB, we find the midpoint of AB, which is C, and trace a line from A to C, or from C to B.

Answer:

x = log (7)/ 2log 5

Step-by-step explanation:

25^ x = 7

Replace 25 with 5^2

5^ 2x = 7

Take log  on each side

log (5 ^2x) = log ( 7)

We know that log a^ b = b log a

2x  log 5 = log (7)

Divide each side by log 5

2x  log 5/ log 5= log (7)/ log 5

2x = log (7)/ log 5

Divide each side by 2

x = log (7)/ 2log 5