Answers
The value of x is 12 and this can be determined by using the arithmetic operations and the given data.
Given :
40% is equal to the fraction x/30.
The following steps can be used in order to determine the value of 'x':
Step 1 - The arithmetic operations can be used in order to determine the value of 'x'.
Step 2 - According to the given data, the 40% is equal to the fraction x/30.
Step 3 - So, the value of X is calculated as:
[tex]\dfrac{40}{100}=\dfrac{x}{30}[/tex]
Step 4 - Simplify the above expression.
x = 12
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Related Questions
if Chelsea has 11 times as many art. Brushes and they have 60 art brushes altogether how many brushes does Chelsea have
Answers
A sum of $5000 is invested at an interest rate of 5% per year. Find the time required for the money to double if the interest is compounded continually. A(t)=Pe^rt
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The time required for the principal amount to double is 13 years 10 months and 10 days approx.
What is compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The term "compound" is crucial here.
CI Formula. C.I. = Principal (1 + Rate)^time − Principal.
Given, A sum of $5000 is invested at an interest rate of 5% per year.
hence, principle = 5000
Amount = 10000
rate = 5%
let's assume the time is x
Let's solve for time
A(t)= 10000 = 5000* e⁵ˣ/¹⁰⁰
2 = (e)^x/20
taking logs on both sides
ln 2 = x / 20
x = 20 ln2
time required = 20 ln2 = 20 * 0.69 = 13.86
Therefore, To make the amount double at the interest rate of 5% we need time approx 13 years 10 months, and 10 days.
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Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. suppose that to qualify for the nationals, a woman must complete the 200-meter backstroke in less than 128 seconds. what proportion of competitive female swimmers will qualify for the nationals? give your answer to four (4) decimal places.
Answers
The probability of a normally distributed data is given by:
[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\bar{x}}{\sigma} \right)[/tex]
Thus, the probability that a woman completes the 200-meter backstroke in less than 128 seconds is given by:
[tex]P(X\ \textless \ 128)=P\left(z\ \textless \ \frac{128-141}{7} \right)=P(z\ \textless \ -1.857)=0.03165[/tex]
Therefore, the proportion of competitive female swimmers who will qualify for the nationals is 0.0317 to 4 decimal places.
(2x^3+2x^2-16x+32)÷(x^2-3x+4) divide polynomial using long division
Answers
_________________________
x^2-3x+4 / 2x^3+2x^2-16x+32
Note that x^2 divides into 2x^3 with a partial quotient of 2x. Multiply x^2-3x+4 by this 2x and write your product under 2x^3+2x^2-16x+32:
__2x _________________________
x^2-3x+4 / 2x^3+2x^2-16x+32
2x^3 -6x^2 + 8x
----------------------- subtract
8x^2 -24x + 32
Now divide x^2 into 8x^2: result is 8.
__2x + 8_________________________
x^2-3x+4 / 2x^3+2x^2-16x+32
2x^3 -6x^2 + 8x
-----------------------
8x^2 -24x + 32
8x^2 -24x + 32
------------------------ subtract
0
So the desired quotient is 2x+8, or 2(x+4).
Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month. The bike Jane wants is $1,536 at the local bike shop.
Which equation represents this situation, and after how many months, t, will Jane have enough money to purchase the bike?
A, 3(2)t = 1,536; t = 11
B, 3(1.2)t = 1,536; t = 35
C, (3 · 2)t = 1,536; t = 9
D, 3(2)t = 1,536; t = 9
Answers
i just did the math. plug 3(2)^9 in to a calculator!
Answer:
Hence, option: D is true.
D) 3×(2)^t = 1,536; t = 9
Step-by-step explanation:
Jane is saving her money in order to purchase a new racing bike. She initially saves $3 and plans to double the amount she saves each month.
he bike Jane wants is $1,536 at the local bike shop.
The equation that represents this situation, and after how many months, t, will Jane have enough money to purchase the bike is:
D) 3×(2)^t = 1,536; t = 9
since in the first month the cost is:
[tex]C_1=3\times 2[/tex]
in next month the cost is:
[tex]C_2=3\times 2\times 2\\\\C_2=3\times 2^2[/tex]
in t=3 months the expression is:
[tex]C_3=3\times 2^2\times 2\\\\C_3=3\times 2^3[/tex]
Hence in general we say:
[tex]C_t=3\times 2^t[/tex]
Hence,
[tex]3\times 2^t=1536\\\\2^t=\dfrac{1536}{3}\\\\2^t=512\\\\2^t=2^9\\\\t=9[/tex]
Hence, option: D is true.
D) 3×(2)^t = 1,536; t = 9
Find the inverse laplace transform of the function by using the convolution theorem. f(s) = 1 s5(s2 + 1)
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[tex]f(t)=(g*h)(t)=\displaystyle\int_{\tau=0}^{\tau=t}g(\tau)h(t-\tau)\,\mathrm d\tau\implies F(s)=G(s)H(s)[/tex]
where [tex]F(s),G(s),H(s)[/tex] are the respective Laplace transforms of [tex]f(t),g(t),h(t)[/tex].
We have
[tex]F(s)=\dfrac1{s^5(s^2+1)}=\dfrac1{4!}\dfrac{4!}{s^5}\times\dfrac1{s^2+1}[/tex]
If we let [tex]G(s)=\dfrac{4!}{s^5}[/tex] and [tex]H(s)=\dfrac1{s^2+1}[/tex], then clearly [tex]g(t)=t^4[/tex] and [tex]h(t)=\sin t[/tex], so by the convolution theorem,
[tex]f(t)=\dfrac1{4!}t^4*\sin t=\displaystyle\frac1{24}\int_{\tau=0}^{\tau=t}\tau^4\sin(t-\tau)\,\mathrm d\tau=\frac{t^4}{24}-\frac{t^2}2+1-\cos t[/tex]
explain -3 1/3, 3.3, -3 and 3/4, 3.5 from least to greatest
Answers
Cory earns $9 per hour working at the local library. If she works 5 hours on Saturday how much money will she earn?
Answers
The length of the base of a rectangle is 6 less than 3 times the width. The perimeter of the rectangle is 52 inches. What is the length of the base?
Answers
what's the length? well, length = 3w - 6.
The isosceles triangle has a perimeter of 7.5m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
Answers
2x=7.5-2.1
2x=5.4
x=2.7
Answer:
2.1 +2x=7.5
Step-by-step explanation:
find the sum of all 3 digit whole numbers that arw divisible by 13 ?
Answers
a0 = 1st 3-digit number divisible by 13
a0 = 104
d = 13 (why?)
last term is largest divisible by 13 = 988
how many terms? (988-104)/13 + 1 = 69
S = 69/2(104+988) = 37674
The sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].
To find the sum of all 3-digit whole numbers that are divisible by 13, we can use the arithmetic series formula.
1. Identify the first and last 3-digit numbers divisible by 13:
- The smallest 3-digit number divisible by 13 is 104 (since [tex]\( 13 \times 8 = 104 \)[/tex]).
- The largest 3-digit number divisible by 13 is 988 (since [tex]\( 13 \times 76 = 988 \)[/tex]).
2. Calculate the number of terms in the series:
- Use the formula for the number of terms n in an arithmetic sequence:
[tex]\[ n = \frac{\text{last term} - \text{first term}}{\text{common difference}} + 1 \][/tex]
Here, the common difference d = 13:
[tex]\[ n = \frac{988 - 104}{13} + 1 = \frac{884}{13} + 1 = 68 + 1 = 69 \][/tex]
3. Find the sum of the arithmetic series:
- The sum [tex]\( S_n \)[/tex] of the first n terms of an arithmetic series is given by:
[tex]\[ S_n = \frac{n}{2} \times (\text{first term} + \text{last term}) \][/tex]
Substitute the values:
[tex]\[ S_{69} = \frac{69}{2} \times (104 + 988) \][/tex]
Simplify the calculation:
[tex]\[ S_{69} = \frac{69}{2} \times 1092 = 34.5 \times 1092 = 37674 \][/tex]
Thus, the sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].
Write 34 13/20 as a decimal please help!
Answers
Use a calculator to divide 13/20.
13/20 = 0.65
34 13/20 = 34 + 13/20 = 34 + 0.65 = 34.65
Find the probability and interpret the results. if convenient, use technology to find the probability. during a certain week the mean price of gasoline was $2.715 per gallon. a random sample of 32 gas stations is drawn from this population. what is the probability that the mean price for the sample was between $2.691 and $2.732 that week? assume sigmaσequals=$0.049
Answers
[tex]\mu=\$2.715 \\ \\ \sigma=\$0.049[/tex]
The probability of a normally distributed data between two values (a, b) is given by:
[tex]P(a\ \textless \ \bar{x}\ \textless \ b)=P\left( \frac{b-\mu}{\sigma/\sqrt{n}} \right)-P\left( \frac{a-\mu}{\sigma/\sqrt{n}} \right)[/tex]
Thus,
[tex]P(\$2.691\ \textless \ \bar{x}\ \textless \ \$2.732)=P\left( \frac{\$2.732-\$2.715}{\$0.049/\sqrt{32}} \right)-P\left( \frac{\$2.691-\$2.715}{\$0.049/\sqrt{32}} \right) \\ \\ =P(1.963)-P(-2.771)=0.97515-0.0028=\bold{0.97235}[/tex]
To find the probability of the sample mean price being between $2.691 and $2.732, calculate the Z-scores for each bound and use a Z-table or statistical software. This utilizes the central limit theorem and the concept of Z-scores in statistics.
Explanation:The question is about finding the probability that the mean price for a sample of 32 gas stations was between $2.691 and $2.732, assuming the population mean was $2.715 and standard deviation was $0.049. To solve this, we use the Z-score formula for each sample mean, Z = (X - μ) / (σ/√n), where μ is the population mean, σ is the population standard deviation, and n is the sample size. Then, we find the area between these Z-scores using a Z-table or statistical software to get the probability.
To calculate:
For $2.691: Z = ($2.691 - $2.715) / ($0.049/√32) = -3.44For $2.732: Z = ($2.732 - $2.715) / ($0.049/√32) = 2.45Refer to a Z-table or software with these Z-scores to find the probability of the sample mean price being between $2.691 and $2.732. This method exemplifies how statisticians use Z-scores and the central limit theorem to estimate probabilities relating to sample means.
the vertex of this parabola is at (3,5). When the y-value is 6, the x-value is -1. What is the coefficient of the squared term in the parabolas equation
Answers
[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex \begin{cases} h=3\\ k=5 \end{cases}\implies y=a(x-3)^2+5 \\\\\\ \textit{we also know that } \begin{cases} y=6\\ x=-1 \end{cases}\implies 6=a(-1-3)^2+5 \\\\\\ 1=a(-4)^2\implies 1=16a\implies \cfrac{1}{16}=a[/tex]
The coefficient of the squared term in the parabola's equation, with a vertex at (3,5) and passing through the point (-1,6), is 1/16.
The student is asking about the coefficient of the squared term in the parabola's equation given that the vertex is at (3,5) and another point on the parabola is (-1,6). Since we know the vertex, we can write the vertex form of a parabolic equation as:
y = a(x - h)
^2 + k
Plugging the vertex into the equation, we get:
5 = a(3 - 3)
^2 + 5
This simplifies down to:
5 = a(0) + 5
So, we cannot determine 'a' from the vertex alone. However, we can use the other point to find 'a'. Plugging the coordinates (-1,6) into the vertex form, we get:
6 = a(-1 - 3)^2 + 5
6 = a(-4)^2 + 5
6 = 16a + 5
1 = 16a
a = 1/16
Therefore, the coefficient 'a' is 1/16.
may i please have some help?
Answers
notice the tickmarks, thus TP = PU and TQ = QS, so the PQ segment is then a midsegment of the larger triangle, and thus the angles it makes on the small one, are exactly the same.
50 points and brainliest
(3^8 x 2^-5 x 9^0) ^-2 x (2^-2 / 3^3) ^4 x 3^28
Write your answer in simplified form. Show all the steps
Answers
(3^8 *2^-5 *9^0)^-2 * (2^-2/3^3)^4 * 3^28 =
(6561 * 0.03125 * 1)^-2 * (0.25/27)^4 * 2.287679245x10^13 =
0.0000237881 * 0.00000000073503 * 2.287679245x10^13 =
0.40000008, round to 0.4
= 3^-16 2^10 x 1^-2 x 2^-8 x 3^-12 x 3^28
= 3^0 x 2^10 x 1^-2 x 2^-8
=1 x 2^2 x 1
= 1 x 4 x 1
= 4
Andrew believes that the probability that he will win the tennis match is 2/9. what is the probability that he will lose the tennis match?
Answers
This is because, in this scenario, a 100% probability is 9/9 and if the probability he will win is 2/9, then the probability he will lose is 9/9-2/9=7/9
Ina case whereby Andrew believes that the probability that he will win the tennis match is 2/9.the probability that he will lose the tennis match is [tex]\frac{7}{9}[/tex]
What is probability?Probability is the likelihood that something will occur. When we're not sure how something will turn out, we can discuss the likelihood of different outcomes, or their probabilities. Statistics is the study of events that follow a probability distribution.
p(he will win the tennis match )= 2/9.
P(he will lose the tennis match) =1 - 2/9
[tex]\frac{9}{9} -\frac{2}{9}[/tex]
=[tex]\frac{7}{9}[/tex]
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Geneva rode her bike a total of 2 1/2 miles from her house to school. First she rode 4/5 mile from her house to the park. Then she rode 1/5 mile from the park to her friends house . Finally she rode the rest of the way to her school? How many miles did she ride from her friends house to school
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Answer:
She rode [tex]1\frac{1}{2}[/tex] miles from her friends house to school.
Step-by-step explanation:
Geneva rode her bike a total = [tex]2\frac{1}{2}[/tex] miles
She rode from her house to the park = [tex]\frac{4}{5}[/tex] miles
She rode from the park to her friend's house = [tex]\frac{1}{5}[/tex] miles
total distance from her house to her friend's house = [tex]\frac{4}{5}+\frac{1}{5}[/tex] = 1 mile
Finally she rode the rest of the way to her school.
distance between her friend's house to school = [tex]2\frac{1}{2}-1[/tex] = [tex]\frac{3}{2}[/tex] miles
[tex]1\frac{1}{2}[/tex] miles she rode from her friends house to school
After a concert for 1,200 people, only 9 people said they would not go to see the band again. What percent of the people who went to the concert said they would not go to see the band again? 0.75% 9% 75% 133%
Answers
divide 9 by 1200
9 / 1200 = 0.0075 = 0.75%
One book costs 95p. How much do five books cost?
Answers
If one book costs 95p, then 5 must cost 5 times 95p.
95*5
=475
Five books would cost 475p.
Hope this helps.
-Benjamin
Sharon earns $25 per item she sells plis a base salary of $100 per week. Write and solve an inequality to finfmd how many items she must selll to earn at least $700per week.
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in a 10x10 grid that represents 800, one square represents
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10x10=100
So, the squares must equal 8 times as many as 10.
So it would be 8.
Suppose that we roll a fair die until a 6 comes up.
a.what is the probability that we roll the die n times
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One half liter of lemonade concentrate is added to 3 liters of water. how many one thirds liter servings of lemonade are made.
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so in short, how many times does 1/3 go into 3 and 1/2?
let's change the mixed to "improper" and divide then.
[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------\\\\ \cfrac{\quad \frac{7}{2}\quad }{\frac{1}{3}}\implies \cfrac{7}{2}\cdot \cfrac{3}{1}\implies \cfrac{21}{2}\implies 10\frac{1}{2}[/tex]
Explain how finding 4x 384 can help you find 4 x 5,384. Then find both products
Answers
so the answer is 21,536
what is the domian of the function y=In (-x+3/2)
Answers
The domain of the function y = ln (-x + 3/2) is all real numbers less than 3/2, represented in interval notation as (-∞, 3/2). This is because the argument of the logarithm must be positive, leading to an inequality that restricts x to be less than 3/2.
Explanation:The domain of a function refers to the complete set of possible values of the independent variable. For the function y = ln (-x + 3/2), we must consider where the argument of the natural logarithm, -x + 3/2, is greater than zero. This is because the natural logarithm function is defined only for positive arguments.
To find the domain, set the argument of the logarithm function greater than zero: -x + 3/2 > 0. Solving this inequality, we find -x > -3/2, hence x < 3/2. This means that the domain of the function is all real numbers less than 3/2, which can be written in interval notation as (-∞, 3/2).
The domain of a function is the set of all possible input values. In the function y = ln(-x + 3/2), the natural logarithm function is defined only for positive numbers, so to find the domain, we need to identify the values of x that make the argument of the logarithm greater than zero.
Solve for the argument inside the logarithm to be greater than zero: -x + 3/2 > 0
Simplify the inequality to find the valid domain: x < 3/2
Therefore, the domain of the function y = ln(-x + 3/2) is x < 3/2.
A company borrowed $25,000 at 3.5% and was charged $2,625 in interest. How long was it before the company repaid the money?
Answers
Answer-
The company repaid the money in 3 years.
Solution-
A company borrowed $25,000 at 3.5% and was charged $2,625 in interest.
Considering the interest as simple interest,
[tex]\text{interset}=\dfrac{\text{Principal}\cdot \text{Rate of interest}\cdot \text{Time period}}{100}[/tex]
Here,
Interest = $2625
Principal = $25000
Rate of interest = 3.5% annually
Putting the values,
[tex]\Rightarrow 2625=\dfrac{25000\times 3.5\times t}{100}[/tex]
[tex]\Rightarrow t=\dfrac{2625\times 100}{25000\times 3.5}[/tex]
[tex]\Rightarrow t=3\ years[/tex]
Therefore, the company repaid the money in 3 years.
Donna opens a certificate of deposit (CD) with $2,000. The bank offers a 3% interest rate. If the account compounds quarterly, which of the following equations represents the future value of the account, after 1 year?
Answers
2) Values:
after 1 quarter: 2000 (1 + 0.03/4)
after 2 quarters: 2000 (1 + 0.03/4)^2
after 3 quarters: 2000 (1 + 0.03/40^4
after 4 quarters = 2000 (1 + 0.03/4)^4
You could have used the future value formula directly:
A = C * (1 + r/n) ^ n*t
where r = 3% = 0.03
n = number of periods in a year: 4
t = number of years = 1
C = initial investment = 20000
=> A = 2000 (1 + 0.03/4)^4
Answer: option D. A = 2000 ( 1 + 0.03 /4) 4
Which ordered pairs in the form (x, y) are solutions to the equation 7x−5y=28 ?Solation 7x−5y=28 ? A. (−6, −14) B. (7,9) C. (4,10) D.(-1,-7)
Answers
pair x y 7x - 5y
A. (-6,-14) -6 -14 7(-6) - 5(-14) = -42 + 70 = 28 => it is a solution
B. (7,9) 7 9 7(7) - 5(9) = 49 - 45 = 4 => not a solution
C. (4,10) 4 10 7(4) - 5(10) = 28 - 50 = - 22 => not a solution
C. (-1,-7) -1 -7 7(-1) - 5(-7) = -7 + 35 = 28 => it is a solution
Answer: option A. (-6,-14) and option D. (-1,-7)
If y has moment-generating function m(t) = e 6(e t −1) , what is p(|y − µ| ≤ 2σ)?
Answers
Now assuming [tex]\mu,\sigma[/tex] denote the mean and standard deviation of [tex]Y[/tex], respectively, then we know right away that [tex]\mu=6[/tex] and [tex]\sigma=\sqrt6[/tex].
So,
[tex]\mathbb P(|Y-\mu|\le2\sigma)=\mathbb P(6-2\sqrt6\le Y\le6+2\sqrt6)=\dfrac{66366}{175e^6}\approx0.940028[/tex]