1. The simple interest rate is 80%
2. The interest earned on the account after 10 years is $75
What is simple interest?Simple interest can be defined as a mathematical or arithmetic method of calculating the charge of interest on a given loan.
The formula for simple interest is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal or initial amountR is the interest rateT is the time taken for the interestFrom the information given, we are to determine the interest rate, R
Substitute the values into the formula, we have;
320 = 200 × R × 2/100
Now, cross multiply, we have;
320(100) = 400R
Find the product of the values
400R = 32000
Divide both sides by the coefficient of the interest rate, we get
R = 32000/400
Find the quotient
R = 80%
If the interest for 2 years is $15
Then in 10 years = $x
cross multiply
x = 150/2
Find the quotient
x = $75
Hence, the rate is 80%
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The Stingrays at the zoo requires the 196 gallon tank to be 4% salt. After a period of time, some water evaporated, raising the salinity to 7%.
How many gallons of water must be resupplied in order to bring the salinity back down to 4%?
Answer:
196 x 3 / 100 = 5,88
Step-by-step explanation:
7% - 4% = 3%
So we need to had 3% t have again 4%
Which expression does not belong with the other three? justify your response.
To find the equation that does not belong with the other three we have to solve each equation.
Given the equation:
[tex]4\cdot x\cdot7=56[/tex]Dividing by 4 at both sides:
[tex]\begin{gathered} \frac{4\cdot x\cdot7}{4}=\frac{56}{4} \\ x\cdot7=14 \end{gathered}[/tex]7:
[tex]\begin{gathered} \frac{x\cdot7}{7}=\frac{14}{7} \\ x=2 \end{gathered}[/tex][tex]5\cdot2\cdot x=40[/tex]Simplifying on the left:
[tex]10\cdot x=40[/tex]10:
[tex]\begin{gathered} \frac{10\cdot x}{10}=\frac{40}{10} \\ x=4 \end{gathered}[/tex]:
[tex]x\cdot3\cdot9=54[/tex][tex]x\cdot27=54[/tex]27:
[tex]\begin{gathered} \frac{x\cdot27}{27}=\frac{54}{27} \\ x=2 \end{gathered}[/tex][tex]4\cdot x\cdot5=40[/tex]4 :
[tex]\begin{gathered} \frac{4\cdot x\cdot5}{4}=\frac{40}{4} \\ x\cdot5=10 \end{gathered}[/tex]5
[tex]\begin{gathered} \frac{x\cdot5}{5}=\frac{10}{5} \\ x=2 \end{gathered}[/tex]In consequence, the equation that does not belong with the other three is:
[tex]5\cdot2\cdot x=40[/tex]because its solution, 4, is different from the solution to the other equations (2).
If we change the 5 in the equation by a 10 and solve the equation we get:
[tex]\begin{gathered} 10\cdot2\cdot x=40 \\ \frac{10\cdot2\cdot x}{10}=\frac{40}{10} \\ 2\cdot x=4 \\ \frac{2\cdot x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]And now the equation (with a 10) belongs with the other three
Heights of 10-year old's, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches.
(a). The height requirement for Batman the Ride is 54 inches. What percent of 10 year old's cannot go on this ride?
(b). Suppose there are four ten year olds. What is the chance that at least two of them will be able to ride Batman the Ride?
(c). Suppose you work at the park to help them better understand their customers demoghraphics, and you are counting people as they enter the park. What is the chance that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park?
(d). What is the chance that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park?
Using the normal distribution and the binomial distribution, it is found that:
a) 43.25% of 10 year old's cannot go on this ride.
b) There is a 0.7814 = 78.14% probability that at least two of them will be able to ride Batman the Ride.
c) There is a 0.1062 = 10.62% probability that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park.
d) There is a 0.0834 = 8.34% probability that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.In the context of this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 55, \sigma = 6[/tex]
For item a, the proportion is the p-value of Z when X = 54, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (54 - 55)/6
Z = -0.17.
Z = -0.17 has a p-value of 0.4325.
Hence the percentage is of 43.25%.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For item b, the parameters of the binomial distribution are given as follows:
p = 0.5675, n = 4.
Hence:
P(X = 2) = 6 x (0.5675)² x (0.4325)² = 0.3615.P(X = 3) = 4 x (0.5675)³ x (0.4325)¹ = 0.3162.P(X = 4) = (0.5675)^4 = 0.1037.Hence:
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3615 + 0.3162 + 0.1037 = 0.7814.
Which is the probability.
For item c, the probability is given as follows:
p x P(X = 0 with n = 2).
Hence:
p = 0.5675 x (0.4325)² = 0.1062.
For item d, the probability is given as follows:
p x P(X = 4 with n = 11). (inverse binomial).
Hence:
0.5675 x (11!)/(5! x 6!) x (0.5675)^4 x (0.4375)^7 = 0.0834.
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Help me answer this.
iven:
here are givren the expression:
[tex](2z-y)^{20}[/tex]xplanation:
o find the coefficient of the given expression, we need to use the binomial expansion formula:
So,
From the formula of binomial expansion:
[tex](x+y)^n=\sum_{k\mathop{=}0}^n(n,k)x^ky^{n-k}[/tex]then,
After using the above formula in the given binomial, the expansion will be:
[tex](2z-y)^{20}=y^{20}-40y^{19}z+760y^{18}z^2-9120y^{17}z^3+77520y^{16}z^4-496128y^{15}z^5+...[/tex]inal answer:
ence , the coefficient of the given term is shown below:
[tex]77520[/tex]I need help with this
Answer:
[tex]\text{ 78 miles per hour}[/tex]Step-by-step explanation:
Given the linear function for the traffic fines:
[tex]f(s)=14(s-60)+40[/tex]If a fine comes to $292, substitute f(s)=292 and solve for "s" to find the speed of the person:
[tex]\begin{gathered} 292=14(s-60)+40 \\ 292=14s-840+40 \\ 14s=292+840-40 \\ 14s=1092 \\ s=\frac{1092}{14} \\ s=78\text{ miles per hour} \end{gathered}[/tex]what picture can you draw to show a thinking about 9÷4?
Think of
[tex]\frac{Green}{Red}[/tex]The area of a circle is 100π cm². What is the circumference, in centimeters? Express your answer in terms of \piπ. THE ACTUAL ANSWER PLEASE
Answer:
35.45
Step-by-step explanation:
C=2πA=2·π·100≈35.44908
Rhianna drew a scale drawing of a house and its lot. She used the scale 9 inches = 5 feet. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
The scale factor that was used for the drawing is 1 inch represents [tex]\frac{5}{9}[/tex] feet.
What is the scale factor?A fraction is a non-integer that has a numerator and a denominator. An example of a fraction is 2/9. 2 is the numerator and 9 is the denominator.
A scale drawing is either a smaller or a bigger version of another image. If the scale used in the drawing is smaller in relation to the dimension of the original image, the scale drawing is a reduced image. If this is not the case, then it is a bigger scale drawing.
The scale drawing is usually reduced at a constant dimensions using a scale factor. In order to determine the scale factor, divide both dimensions provided by 9.
(9 / 9) = (5 / 9)
1 inch = 5/9 feet
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Describe and correct the error in evaluating the expression.
9 + 2 x 3 = 11 x 3 = 33
How would you write this problem with the multiplication first?
The error in the solution is adding 9 and 2 before the multiplication and the new expression is (2 x 3) + 9
The description of the error?The equation and the steps are given as
9 + 2 x 3 = 11 x 3 = 33
The above solution is incorrect
This is so because the product has a higher order of precedence
So, it must be evaluated first
So, the correct solution is
9 + 2 x 3 = 9 + 6 = 15
To rewrite the expression such that the product is done first, we introduce the use of brackets
So, we have
9 + (2 x 3)
This gives
(2 x 3) + 9
Hence, the result of the products is (2 x 3) + 9
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the lewis family drove 45.6 miles to the river. It took them 1.2 hours to get there. How fast did they drive? Round to the nearest whole number
The most appropriate choice for speed will be given by
Speed of the car of Lewis family = 38 miles/hours
What is speed?
Distance travelled by an object per unit of time is called speed.
If d is the distance travelled and t is the time taken, then speed is calculated by-
Speed = [tex]\frac{d}{t}[/tex]
Here, speed is a scalar as the direction is not taken into account.
Distance drove by Lewis family to the river = 45.6 miles
Time taken by the Lewis family to go to the river = 1.2 hours
Speed of the car of Lewis family = [tex]\frac{45.6}{1.2}[/tex]
= 38 miles/hour
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In a recent year, there were 29,757 traffic fatalities in the United States. Of these, 9001 were alcohol related.
(a) What is the probability that a bandomly selected traffic fatality in this year was alcohol related?
(b) What is the probability that a randomly selected traffic fatality in this year was not alcohol related?
(c) What is the probability that two randomly selected traffic fatalities in this year were both alcohol related?
(d) What is the probability that neither of two randomly selected traffic fatalities in this year were alcohol related?
(e) What is the probability that of two randomly selected traffic fatalities in this year, at least one was alcohol related?
we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.
Total traffic fatalities = 29,757
Alcohol related = 9001
(a) probability that a randomly selected traffic fatality in this year was alcohol related:
P = 9001 / 29,757 = 0.302
(b) probability that a randomly selected traffic fatality in this year was not alcohol related:
P = 1 - 0.302 = 0.698
(c) probability that two randomly selected traffic fatalities in this year were both alcohol related:
P = 0.302 × (9000 / 29756)
P = 0.091
(d)What is the probability that neither of two randomly selected traffic fatalities in this year were alcohol related:
P = 1 - 0.091
P = 0.909
(e) probability that of two randomly selected traffic fatalities in this year, at least one was alcohol related
P = 0.302 + 0.302 = 0.604
Therefore, we have found out the probability for different cases when there were 29,757 traffic fatalities in the United States and of these, 9001 were alcohol related.
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Find the measure of arc indicated using the inscribed angle given in thecircle below.X91 0YZ?
SOLUTION
The correct option is A (the first option)
We are asked to find the measure of the angle at the center.
Circle theorem:
The angle at the center of a circle = 2 x Angle at the circumference
The angle at the center of the circle = 2 x = 2 x 91 degrees
=182 degrees
The value for the angle at the center (?) of this circle is
[tex]182^o[/tex]The correct option is A (the first option)
HELP ME PLEASE SOON NEED RN
Answer:
x = + or - 8
Step-by-step explanation:
2x^2 = 128
solve for x
hope this helped have a great day ^^
Help
Simplify the negative exponent. Please show your work.
4 ⁻⁴
Answer: 0.0625
Step-by-Step Explanation: positive exponents = multiply the number by itself however many times the exponent demands.
negative exponents: multiply the reciprocal of the base number by itself however many times the exponent demands.
Solve similar triangles (advanced) khan academy. solve for x
Answer:
that would be X=22, i had the same thing today, and got it right :D
Step-by-step explanation:
The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?
If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
Consider the width of the rectangle as w
The length of a rectangle is 3 cm less than twice the width of the rectangle
The length of the rectangle = 2w-3
Perimeter of the rectangle = 75 cm
Perimeter of the rectangle =2(l+w)
Where l is the length and w is the width of the rectangle
Substitute the values in the equation
2(2w-3+w) = 75
2(3w-3) = 75
6w-6 = 75
6w = 81
w = 13.5 cm
The length of the rectangle = 2(13.5)-3
=24 cm
Hence, If the length of a rectangle is 3 cm less than twice the width of the rectangle and the perimeter is 75 cm, then the length is 24 cm and width is 13.5 cm
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X+4y=10 and 3x-y=-9 find the value of x/y
[tex]x = 10 - 4y.....(3)[/tex]
I WILL SOVE BY SUBSTITUTION.
[tex]3(10 - 4y) - y = - 9 \\ 30 - 12y - y = - 9 \\ - 13y = -9 - 30 \\ - 13y = - 39 \\ \frac{ - 13y}{ - 13} = \frac{ - 39}{ - 13} \\ y = 3 \\ [/tex]
[tex] x= 10 - 4(3) \\ x = 10 - 12 \\ x = - 2[/tex]
we have (-2,3)
ATTACHED IS THE SOLUTION
Write .24 as a fraction
in lowest terms.
Answer:
.24 as a fraction is 6/25
Step-by-step explanation:
1) Let convert our decimal into a percentage so we could write it in the not simplified fraction of 0.24:
.24 = 24% = 24/100
2) Now since we have 24/100, we could now simplify:
24/100 = 12/50 = 6/25
We can't simplify anymore.
Answer: 6/25
Step-by-step explanation:
Find the x-intercept of the line that passes through (-3,4) and is perpendicular to the graph of x-2y=7
Answer:
x - intercept = - 1
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 - 2y = 7 ( subtract x from both sides )
- 2y = - x + 7 ( divide through by - 2 )
y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{7}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation of the perpendicular line\to find c substitute (- 3, 4 ) into the partial equation
4 = 6 + c ⇒ c = 4 - 6 = - 2
y = - 2x - 2 ← equation of perpendicular line
to find the x- intercept let y = 0 into the equation and solve for x
- 2x - 2 = 0 ( add 2 to both sides )
- 2x = 2 ( divide both sides by - 2 )
x = - 1
the x- intercept of the perpendicular line is - 1 or (- 1, 0 )
A pedestrian signal at a crosswalk has the following cycle: "WALK” for 45 seconds, "DON'TSTART" for 30 seconds and "DONT WALK" for 40 seconds. What is the probability the signalwill show "DON'T START" if you arrive at a random time? Write your answer as a percentagerounded to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
The probability is represented by the following equation:
[tex]undefined[/tex]15. Over what range of angles does the value of sin(O) consistently increase?
A. 45° to 135°
B. 90° to 180°
C. 0° to 180°
D. 0° to 90°
The value of sin(O) will at the range of 0° to 90° consistently increase. This makes option D the correct options.
how to find the range of values where sin will consistently increaseIn trigonometry, the first basic functions are the sin, cos and tan.
In a right angle triangle the sin is represented as the ratio of opposite to hypotenuse. cos is represented as the ratio of the adjacent to hypotenuse, while tan is the ratio of opposite to adjacent or ratio of sin to cos.
Plotting the graph of sin functions, the pattern forms a sinusoidal pattern which bears its maximum value at sin 90degrees and the minimum value at sin 0 degrees.
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The proof is converted to paragraph form.
Which parts of the paragraph proof are incorrect?
The part "since ∠ AMC is a right angle, ∠BMC and ∠CMD will be complementary" and "since ∠ BMC is a right angle, ∠BMC and ∠AMB will be complementary" , the paragraph proof is incorrect.
We are given that,
∠ AMC and ∠BMC are right angles.
Since,
∠ AMC = ∠ AMB + ∠ BMC
The paragraph part should have been ∠ AMB and ∠ BMC are complementary angles and,
Since,
∠ BMD = ∠ BMC + ∠ CMD
The paragraph part should have been ∠ CMD and ∠ BMC are complementary angles instead of the part given in the paragraph proof.
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Can someone please help me with this geometry question
Jason made a spherical cake pop that is 1.3 inches in diameter. He coated the whole cake pop with sprinkles.What is the approximate area Jason covered with sprinkles?
Given:
The diameter of the sphere is 1.3 inches.
The surface area of the sphere is given as,
[tex]\begin{gathered} SA=4\pi\times r^2 \\ SA=4\pi\times(\frac{d}{2})^2 \\ SA=4\pi\times(\frac{1.3}{2})^2 \\ SA=1.69\pi \\ SA=1.69\times3.14\ldots\ldots\pi=3.14 \\ SA=5.3066 \\ SA\approx5.3\text{ square inches} \end{gathered}[/tex]Answer: area covered with sprinkles is 5.3 square inches
what does this mean 3|-3| the whole |-3| thing I'm confused please help
|-3| means "the absolute value of 3", which is a way of saying how far away from zero the number -3 is on the number line.
The definition of absolute value goes like this:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
In other words, if the number [tex]x[/tex] inside the absolute value bars is already positive or zero, we leave it alone. If instead [tex]x[/tex] is negative, we multiply it by -1 to recover the positive version of that number.
Since -3 is negative, it follows that |-3| = -(-3) = 3. So the expression 3 |-3| is equivalent to 3 • 3 = 3² = 9.
Two numbers are respectively 60% and 20% of a third number, second number exepress ss as a perentage of first is?
Answer:
10%
Step-by-step explanation:
this is because the total number is supposed to be 100%
and 60%+20%=90%. 100%-90%=10%.
So 10% is the final answer
13. Making an argument. Your friend claims that a line always represents a function. Is your friend
correct? Explain your reasoning
Based on the given argument, it is concluded that my friend's reasoning was incorrect.
What is a Linear Function?This refers to the type of function that represents one line on a linear plane in cartesian mathematics.
With this in mind and from the claim of my friend that a line always represents a function, my friend is incorrect because If the line was vertical, then it could not pass through and as such, cannot represent a function.
Therefore, the answer to the question is that my friend is incorrect in his claim about lines and functions.
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Which of the following equations best represents "y is inversely related to x"?
y = kx
y = kx2
y = k(1/x)
y = k(1/x2)
and i dont think it is c
The equations best represents "y is inversely related to x" is y = k(1/x).
What is an inverse proportionality?The inverse proportionality can be described as the relationship that exist between two or more quantities whereby when one of the quantities is increasing in value, then the the second quantity will be decreasing in value however there will be a proportionality constant that would be found in the equation.
Considering the chosen option D, we can see that when the value of y is increasing then the value of x will be decreasing, and when the value of x is decreasing , them the value of y will be increasing.
Therefore, option C is correct.
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Where do you find a vertical shift in the exponential parent function?
What happens when (x-4) is in the exponent?
What happens when (x+9) is in the exponent?
Where do you find a horizontal shift in the exponential parent function?
What happens when there is a +7 at the end of the exponential parent function?
What happens when there is a -6 at the end of the exponential parent function?
For the given expressions we will have:
y = exp(x - 4) →we have a shift of 4 units to the right.
y = exp (x +9) → we have a shift of 9 units to the left.
y = exp(x) + 7 → we have a shift of 7 units up.
y = exp(x) - 6 → we have a shift of 6 units down.
How to work with vertical and horizontal shifts?
Remember that the shifts work as follows.
For a function f(x), we define a vertical shift of N units as:
g(x) = f(x) + N
If N > 0, the shift is upwards.If N < 0, the shift is downwards.For a function f(x), we define a horizontal shift of N units as:
g(x) = f(x + N)
If N > 0, the shift is to the left.If N < 0, the shift is to the right.Then, if we have:
exp(x - 4) we have a shift of 4 units to the right.
exp (x +9) we have a shift of 9 units to the left.
exp(x) + 7 we have a shift of 7 units up.
exp(x) - 6 we have a shift of 6 units down.
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The sum of a number and 4
The solution for x in the equation x + 4 = 12 is 8.
Given,
Sum of two numbers is 12
Take the first number as x
Second number is given as 4
We have to find the value of x.
The equation will be like:
x + 4 = 12
Solve for x in the equation.
Add -4 to both sides
x + 4 - 4 = 12 - 4
x = 8
That is, the solution for x in the equation x + 4 = 12 is 8.
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The question is incomplete. Completed question is given below.
The sum of a number and 4 is 12. Find the number.