The equation and solution representing the total interest, T, earned by Kalia when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10, is D. T = 100 • 0.01 • 10; $10.
What is the simple interest?Simple interest is interest that does not compound.
Simple interest does not accumulate interest, unlike compound interest, which is added to the principal for subsequent interest.
Principal = $100
Simple interest rate = 1%
Period of savings = 10 years
The simple interest in dollars = T
T = 100 x 0.01 x 10
T = $10
Thus, Option D correctly represents the total interest earned by Kalia.
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Exercise
1. If you have a case where n=25 and P=0.04, what is the probability that x is equal to 4?
If [tex]n=25[/tex] and [tex]p=0.04[/tex], then the probability of [tex]P(X=4)[/tex] is found to be 0.001374.
What is Binomial Distribution?
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability, [tex]p[/tex]) or failure (with probability, [tex]q=1-p[/tex]).
How to Find the Probability of a Binomial Distribution?
The chance of failure raised to the power of the difference between the number of tries and the number of successes is multiplied by the probability of success raised to the power of the number of successes in order to compute the binomial distribution. Next, multiply the final result by the sum of the number of attempts and the number of successes.The formula for binomial distribution is given as, [tex]P(X=k)={n \choose k}p^{k}(1-p)^{n-k}[/tex]From the given question, we have, [tex]n=25[/tex] and [tex]p=0.04[/tex]
Here, have to find the probability of [tex]P(X=4)[/tex], so [tex]k=4[/tex]
The binomial distribution formula is, [tex]P(X=k)={n \choose k}p^{k}(1-p)^{n-k}[/tex]
Substituting the given values in the above equation, we get
[tex]P(X=4)={25 \choose 4}0.04^{4}(1-0.04)^{25-4}[/tex]
[tex]\implies P(X=4)=12650 \times0.00000256\times0.4243\\\implies P(X=4)=0.001374[/tex]
Therefore, the value of [tex]P(X=4)=0.001374[/tex]
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If you roll a die 75 times. How many 1's should you expect to roll?
step by step explanation to-4x = -x + 3
The value of x is -1 for equation -4x = -x + 3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -4x = -x + 3
In the given equation minus four times of x equal to minus x plus three
x is the variable
Plus and minus are operators
-4x = -x + 3
Take the variables to one sides
Add +x on both sides
-4x+x=-x+x+3
-3x=3
Divide both sides by -3
x=-1
Hence, the value of x is -1 for equation -4x = -x + 3
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Show that the terms of the series ∑n=1log 5r are in AP. Hence, find the sum of the first twenty terms of the series and also the least value of n for which the sum to n terms exceeds 400
The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
We have been given that the terms of the series ∑n=1log 5r are in AP.
As per the given question,
∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)
n = 20
∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)
Using the property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))
∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)
∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)
Using property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(Sr)=20·1og(5)+log(1×2×3×...20)
∑log(5r) = 20-log(5)+log(201)
∑log(5r) = 32.365524703598
Rounded to the nearest hundredth decimal,
∑log(5r) = 32.37
Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.
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126=2×3×3×k
Solve for k
[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]
Step-by-step explanation:-
[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]
[tex]{ \sf{126 = 18 \times k}}[/tex]
[tex]{ \sf{126 = 18k}}[/tex]
Divide both the sides by 18 in order to find the value of k. Then,
[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]
[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]
A straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form. 8 in. 5 in. 5 in.
The length of the straw fitted in the box is 10.67 inches.
What is cuboid?A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.
Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,
Diagonal of a cuboid = √ l² + w² + h²
Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in
Hence, The length of the straw fitted in the box is 10.67 inches.
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The equation for line t can be written as y+3= 1/2(x–7). Line u, which is perpendicular to line t, includes the point (3,3). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation of a line u perpendicular to line t and passes through (3, -3) is y = -2x + 3
How to represent the slope of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptLine t has equation as y + 3 = 1 / 2 (x - 7).
Line u is perpendicular to line t and it passes through (3, -3).
The products of the slope of perpendicular lines is equals to negative 1.
Therefore,
m₁ m₂ = -1
1 / 2 m₂ = -1
m₂ = -2
Therefore, the equation of the line have a slope of -2.
let's find the y-intercept using (3, -3)
-3 = -2(3) + b
b = -3 + 6
b = 3
Therefore, the equation in slope intercept form is y = -2x + 3.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36
What is Equation of Circle?The location of a circle in the Cartesian plane is represented by a circle equation. We can write the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.
The standard equation of a circle with center at
(a, b) and radius is r.
So, the standard equation circle is
(x -a)² + (y- b)² = r²
Given:
As, we know the standard form for equation of a circle is
(x-a)² + (y-b)² = b =r²
where (a, b) is the center of the circle and r is the radius of the circle.
We have
diameter = 12 units
radius = 12/2 = 6 units
So, the center will be at (0, 3)
Thus, the equation of circle
(x-0)² + (y-3)² = 6²
x²+ (y-3)² = 36
Hence, the Equation of Circle is x²+ (y-3)² = 36.
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ERROR ANALYSIS Describe and correct the error in finding m/1. X 115° +39° + m/1 = 360° 154° +m1 = 360° m1= 206
Find the values of x and y
X= 20 & Y= 70 in right-angled triangle .
What is right angle triangle?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. Perpendicular and the triangle's base make up the sides that the right angle is formed from. The longest of the three sides, known as the hypotenuse, is the third side.2X + 140 = 180
2X = 40°
X = 20°
X + Y = 90°
Y = 70°
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List all possible rational roots for the given equation. x^4 - 2 x^2 + 16 x - 15 = 0
The possible roots for the given equation are, -1,3, -1-2i, -1+2i.
What do you mean by the roots of an equation?
The values of the variable that fulfill the equation are known as the roots of a quadratic equation. In addition, they are referred to as the "solutions" or "zeroes" of the quadratic equation. For instance, x = 2 and x = 5 satisfy the quadratic equation x2 - 7x + 10 = 0 and are hence the roots of the equation.
F(x) = x4-2x2-16x-15 has a root (zero) that you should find.
Finding x values for which F(x)=0 is the goal of the Polynomial Roots Calculator method set.
A tool from the list above is the rational roots test. Only numbers x that can be represented as the quotient of two integers, or rational roots, would be found.
According to the Rational Root Theorem, P and Q are factors of the Leading Coefficient and the Trailing Constant, respectively, if a polynomial zeroes for a rational number P/Q.
The Leading Coefficient is 1 and the Trailing Constant is -15 in this instance.
The component(s) are:
1 is the Leading Coefficient, while 1 is the Trailing Constant.
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Solve for x.
-8x+14 ≥ 60 OR - 4x + 50 < 58
Choose 1 answer:
(A
E
x≤-
x≤
-
23
4
23
4
x>-2
or x>-2
There are no solutions
All values of a are solutions
Answer:
[tex]x\leq -7 or x > -2[/tex]
Step-by-step explanation:
-8x+14 ≥ 60 or - 4x + 50 < 58
-8x ≥ 56 or - 4x < 8
[tex]x \leq -7[/tex] or [tex]x > -2[/tex]
I need help with solving problem.
Answer:
i can help but first what the questions and where are the options?
Step-by-step explanation:
Please help asap!! Please please please
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
What is the similarity test of two triangles?
If the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal, the two triangles are similar.
In the given figures, the length of side AB is equal to the length of side DE.
Side AB = Side DE ----------(I)
Similarly, the length of side BC is equal to the length of side EF.
Side BC = Side EF ----------(II)
And the measure of angle ABC is equal to the measure of angle DEF.
∠ ABC = ∠ DEF -------(III)
From (I), (II), and (III), and by using the SAS test we can say that
ΔABC ~ ΔDEF ----------- SAS test
Hence,
Yes, I agree with Jorge.
Jorge's reasoning states that if two sides of the triangles are similar with a common measure of angle then one triangle can fit/overlap with the other triangle.
Jorge could improve his proof by stating his explanation in terms of mathematics.
He could have used the SAS similarity to show that the given triangles are similar.
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X/-9 = 3
X equals what?
Answer:
X=-27
Step-by-step explanation:
X/-9 = 3
(-9) * X/-9 =(-9) * 3
X=(-9) * 3
X=-27
Answer:
x=-27
Step-by-step explanation:
x/-9=3
Multiply each side by -9
x=-27
That's it!
Day
(t) No. of Calories
Burned
C(t)
2 314
4 356
6 370
8 386
10 405
12 442
14 516
Amanda goes to the gym every day and cross–trains. Based on a chart at the gym showing the calories expended for various activities, Amanda has kept track of the number of calories she has burned over the last two weeks. She wants to find the rate at which she burned calories on day 8. That is, she needs to find C'(8). Estimate the value.
A.
8.00 calories per day
B.
8.75 calories per day
C.
17.50 calories per day
D.
17.75 calories per day
Answer: In photo below
You're Welcome :)
If she wants to find the rate at which she burned calories on day 8. C'(8) is: B. 8.75 calories per day
How to find the calories per day?First step is to find the upper and lower values for the burned calories on day 8.
Upper value (C'(8) = 405 - 386 /2
Upper value C'(8) = 19/2
Upper value C'(8) = 9.5
Lower value C'(8) = 386 -370/2
Lower value C'(8) = 16/2
Lower value C'(8) = 8
Now let find C'(8)
C'(8) = 9.5+8/2
C'(8) = 17.5/2
C'(8) = 8.75 calories per day
Therefore the correct option is B.
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Which of the following is NOT true about the body mass index? A. uses statistical data of weight and height across the population B. measures the percentage of one's body fat directly C. relies on a correlation between weight and body fat D. does not account for one's body frame size or muscle content Please select the best answer from the choices provided. A B C D Mark this and return
The statement that is not true about body mass index is B. measures the percentage of one's body fat directly
What is Body mass index?The Body Mass Index (BMI) calculates a person's weight in relation to their height. It is not a precise assessment of a person's total body fat, more of an indicative.
The majority of the time, total body fat and BMI are correlated.
The Body mass index (BMI) formula
= weight in kilograms / square of height in meters
BMI Categories values are classified below
Underweight ≤ 18.5
Normal weight = 18.5–24.9
Overweight = 25–29.9
Obesity = BMI of 30 or greater
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Answer:B
Step-by-step explanation:
litterly help asap
The retail price of a golf club is $342. If the golf store has marked up the price by $42, what is the markup rate?
A golf club costs $342 at retail. The markup rate is 71.4% if the golf store has increased the price by $42.
What is meant by markup rate?The markup percentage is the difference between what an item costs the seller and what the customer pays. The greater the markup, expressed as a percentage of the cost, the greater the profit. While there is no "ideal" markup percentage, most businesses set it at 50%. A 50 percent markup, also known as a "keystone," means you are charging a price that is 50% higher than the cost of the good or service. Both terms are used to help determine profitability, but they are not the same! The markup is the percentage difference between a product's selling price and its cost.Given,
The difference in prices is $342 - $42 = $300
So, we need to find what percentage of 42 is 300
We do this by dividing: 300/42 = 7.14
which is 71.4 %.
So, the markup is 71.4 %.
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11 subtracted from the sum of 7y and 2y is -38.
Answer: 7y = 38.11111111111 2y = 10.8888888889 the sum of these two equals to 49 so 11-49=-38 Hopefully you understood. But I didn't know what you wanted to know from this?
Step-by-step explanation: 11-(7y+2y)=-38
7y+2y=9y (basic math)
11-9y=-38 then you want to move -38 to the other side, and when you move it to the other side it changes its value then from -38 it becomes 38. Same for the -9y, we move it to the other side and it changes its value so now from -9y its 9y. So now are equation should look like this 11+38=9y. 11+38=49 => y=49÷9 y=5.44444444444 (49÷9) x 7 = 38.1111111111 and (49÷9) x 2 = 10.8888888889
Which question can be answered by finding the quotient of 5/6 divided by 1/20?
The question that can be answered by finding the quotient of 5/6 divided by 1/20 is C. Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag. How many bags can he make?
How to illustrate the information?It should be noted that the quotient is the value that is gotten when we divide the numbers given.
In this case, Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag.
The number of bags will be:
= 5/6 ÷ 1/20
= 5/6 × 20
= 100 / 6
= 17 bags
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Answer:
17 bags
Step-by-step explanation:
What other congruence is needed to prove that △QRP≅△QFP by ASA?
QR≅QF
∠R≅∠F
∠QPR≅∠QPF
PR≅PF
Rebecca wants to buy a new phone. She has already saved $110 and received a gift of $50 from her grandmother that she added to her savings. She plans to earn the rest by selling necklaces for $5 each. The phone she wants to purchase costs $485. Write an equation that represents how many necklaces Rebecca will need to sell in order to have enough money to get her phone.
Answer:
Step-by-step explanation:
She needs to sell 65 necklaces.
-353.92 - (-283.56) -131.29
-353.92-(-283.56)-131.29= -20,165
Identify the values of the variables. Give your answers in simplest radical form. Please help!
The values of the variables as represented in the right triangle are; (8√15)/3 and s = (4√15)/3.
What are the values of the variables in the given task content?It follows from the task content that the values of the variables in the right triangle are to be determined.
It follows from trigonometric ratios that;
Sin (∆) = opposite / hypothenuse
Cos (∆) = adjacent / hypothenuse
Tan (∆) = opposite / adjacent
It therefore follows from the attached image that;
Sin (60) = 4√5 ÷ p
p = 4√5 ÷ √3/2
p = (8√15)/3.
Also;
Tan (60) = 4√5 ÷ s
s = 4√5 ÷ √3
s = (4√15)/3
Therefore, the value of the variables are; p = (8√15)/3 and s = (4√15)/3.
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Which expression shows the distance you would drive from the library to the grocery
store along this road?
|-5+7)
-151+171
-5+7
1-5+171
Library Home
CLEAR
Grocery
Store
CHECK
Answer:
1-5+171
Step-by-step explanation:
The Finnish lottery draws 7 numbers from a total of 40 numbers.
What is the probability for a single lottery ticket to have 1 correct?
The probability that a single lottery has one correct number, using the hypergeometric distribution, is of:
0.4159 = 41.59%.
What is the hypergeometric distribution formula?The probability mass function of the hypergeometric distribution is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the function are listed as follows:
x is the number of successes in a single trial.N is the size of the population.n is the size of the sample selected in a single trial.k is the total number of desired outcomes.In the context of this problem, the values of these parameters are given as follows:
N = 40, k = 7, n = 7.
The probability that a single lottery has one correct number is P(X = 1), hence x = 1 and the calculation is as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,40,7,7) = \frac{C_{7,1}C_{33,6}}{C_{40,7}} = 0.4159[/tex]
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2 step equation:12. Amy wants to start taking gymnastics. There is a one-time fee of $35 to sign up, then it costs $85 per month. If Amy saves up $225, how many months of gymnastics can she take?
The number of months Amy can take the Gymnastic = 2 months.
Amy wants to start taking gymnastics.
The fee structure of the gymnastics is divided into two parts.
There is a one time fee payment of 35$ and there is a monthly payment that costs 85$ per month.
So the first month fee of the gymnastics = 35 + 85 = 120$
Savings of Amy = 225$
If Amy pays the 1st month fee ,
then the she will be left with the savings = 225$ - 120$ = 105 $
It means Amy can join the gymnastics for one more month .
Hence the number of months Amy can take the Gymnastic = 2 months .
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0°F; drops 15° what’s the new temperature
The new temperature is given as -15°F.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The present temperature is 0°F.
And, the drop in the temperature is 15°.
The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,
0 - 15°F
= -15°F
Hence, the new temperature after the drop is -15°F.
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Michel is taking 4 credit hours of courses at his local community college. Each credit hour costs $110.50. He is also to pay three technology fees of $19.25. Determine the total amount that he will pay in tuition.
Total: 499.75
Step-by-step explanation:
4 × 110.5 = 442
3 × 19.25 = 57.75
442 + 57.75 = 499.75
Apples cost 1.85 per kilogram
Work out the cost of 1.6 kilogram of apples
for 20 points
Answer:
1.6 kg = $2.96
Step-by-step explanation:
The given statement is,
→ 1 kg of apple = $1.85
→ a = 1.85
Now the cost of 1.6 kg of apple is,
→ 1.6 × a
→ 1.6 × 1.85
→ $2.96
Hence, 1.6 kg of apple is $2.96.