Percent is given by the expression:
[tex]\begin{gathered} \text{Total}\cdot\frac{\text{percent}}{100}=\text{Equivalent number to the percent} \\ 850.8\cdot\frac{x}{100}=221.21 \\ x=\frac{221.21\cdot100}{850.8} \\ x=26\text{ percent} \end{gathered}[/tex]So, he is paying 74% more using the quarterly rate
Which set can represent the side lengths of a right triangle?
The set that represents a right triangle has to satisfy Pythagorean's Theorem where the greatest side is the hypothenuse. Let's evaluate each of them until we get the right set.
[tex]\begin{gathered} 7^2=6^2+(\sqrt[]{21})^2 \\ 49=36+21 \\ 49=57 \end{gathered}[/tex][tex]\begin{gathered} (5\sqrt[]{3})^2=7^2+5^2 \\ 25\cdot3=49+25 \\ 75=74 \end{gathered}[/tex][tex]\begin{gathered} (2\sqrt[]{5})^2=4^2+2^2 \\ 4\cdot5=16+4 \\ 20=20 \end{gathered}[/tex]As you can observe, set B satisfies the theorem.
Hence, B is the answer.The standard normal curve is grafted below. Shade the region under the standard normal curve to the left of x=1.00Use the table to find the area under the standard normal curve to the left of x=1.00
Explanation
Part A
The shaded area under the standard normal curve to the left of z=1.00 can be seen below.
Part B
Using the z table, the area under the standard normal curve to the left of z.=1.00 is
Answer: 0.8413
Choose the equation below that represents the line passing through the point (2, -4) with a slope of(1 point)Oy=kx-3Oy -x+5Oy-1x+3Oy=1x-5
The equation of a line in slope-intercept form can be written like this:
y = mx + b
Where m is the slope and b is the y-intercept of the line.
In this case, the slope of the line is 1/2, then we can rewrite the above equation like this:
y = (1/2)x + b
We are also told that this line passes through (2, -4), by replacing 2 for x and -4 for y into the above equation, we can solve for the value of b, like this:
-4 = 2(1/2) + b
-4 = 1 + b
-4 - 1 = 1 - 1 + b
-5 = b
b = -5
Then, we can rewrite the equation of the line, like this:
y = (1/2)x - 5
Then, the last option is the correct answer
Is Ari’s answer to the question, correct? If not, where did Ari make a mistake? If his answer is incorrect, explain what the correct answer is and why it is correct.
None of Ari's answer to the question is correct. The right application of the laws of exponents to get the correct answer is explained below.
What are the Laws of Exponents?Some of the laws of exponents can be summarized as follows.
The product law of exponents: This states that we are to add the exponents together if we are multiplying two numbers that have the same base. For example, [tex]x^m \times x^n = x^{m + n}[/tex].The division law of exponents: this states that when dividing two numbers that have the same base, we are to find the difference of their exponents. For example, [tex]\frac{x^m}{x^n} = x^{m - n}[/tex].The negative law of exponents: This state that, [tex]x^{-m} = \frac{1}{x^m}[/tex].Based on the above laws of exponents, none of Ari's answer is correct. Below are the correct way to solve the questions:
1. [tex]4^2 \times 4^5 = 4^{2 + 5} = 4^7[/tex]
2. [tex](2^{-5})^3 = 2^{-3 \times 5} = 2^{-15} = \frac{1}{2^{15}}[/tex]
3. [tex]\frac{(\frac{1}{4})^4 \times (\frac{1}{4})^5 }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^{4 + 5} }{(\frac{1}{4})^3} = \frac{(\frac{1}{4})^9 }{(\frac{1}{4})^3} = (\frac{1}{4})^{9 - 3}} = (\frac{1}{4})^6[/tex]
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which of the following would be an acceptable first step in simplifying the expression?
Solution:
Given:
[tex]\frac{cos\text{ }x}{1-sin\text{ }x}[/tex]The only acceptable first step in simplifying the expression from the options that would not change or alter the values of the expression is by multiplying (1 + sin x) to both the numerator and the denominator.
Therefore, the correct answer is OPTION B.
A diesel train left Abuja and traveled west. One hour later a freight train left traveling 50 mph faster in an effort to catch up to it. After three hours of freight train finally caught up. Find the diesel train’s average speed.
The speed at which diesel train was moving is = 150mph
In the above question, it is given that,
Let the speed of the diesel train which left Abuja be x mph
then, speed of freight train which is moving 50 mph faster than diesel train = (50 + x)mph
Further, the freight train finally caught up the diesel train after three hours
So time taken by freight train = 3 hours
While time taken by diesel train would 1 hour more than freight train as its moving slower = 3 + 1 = 4 hours
Now, it is given that both the trains finally catch up, it means the distance travelled by both the trains would be equal
We know that,
Speed = [tex]\frac{Distance}{Time}[/tex]
Distance = Speed x Time
Distance travelled by Diesel train = distance travelled by Freight train
4x = 3(50 + x)
4x = 150 + 3x
x = 150 mph
Hence, the speed at which diesel train was moving is = 150mph
While, the speed at which freight train was moving is = (150 + x)mph = (150 + 50)= 200mph
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help video S-(x – 6)² +7 for 2 2 +3 x = 3 for Find f(3)
Explanation:
This is a function defined by parts. When x is not 3, the function has the equation on top, but when x is 3, the function has one value: 2.
Answer:
f(3) = 2
Write the following numbers in decreasing order: −4; 1 2/3 ; 0.5; −1 3/4 ; 0.03; −1; 1; 0; -103; 54
Decreasing order means from largest to smallest
The ordered list is:
54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103
A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced. Find P(red, then blue).
5 + 6 + 4 = 15
red is 6/15 then taken out
then blue is 5/14
6/15 * 5/14 = 1/7
1/7 or about 0.143
a cyclist rides her bike at a speed of 30 kilometers per hour. what is the speed in miles per hour? how many miles will the cyclist travel in 5 hours?
Answer:
the answer is 9.321 miles
Identify the x intercept(s) from the graphType your answer using set notation {x,x} listing x values in order from least to greatest
The x-intercept is where the graph passes the x-axis.
The graph extends from {-5 ≤ x ≤ 3}
The x-intercept is {x = -1}.
64XOA. VZ is the smallest side.OB. vz is the longest side.OC. XV is the smallest side.OD. XV is the longest side.5759Z
SOLUTION
The triangle XYZ shown below :
The angle with the longest side is said to be the angle with the largest angle:
The largest angle faces the longest side
Hence the Option B is t
[tex]YZ=x=longest\text{ side}[/tex]Can you please help me because I don’t understand this and I would like to really understand it
Answer:
Explanation:
Given the expression:
[tex]\sqrt{12(x-1)}\div\sqrt{2(x-1)^{2}}[/tex]By the division law of surds:
[tex]\sqrt[]{x}\div\sqrt[]{y}=\sqrt[]{\frac{x}{y}}[/tex]Therefore:
[tex]\sqrt[]{12(x-1)}\div\sqrt[]{2(x-1)^2}=\sqrt[]{\frac{12(x-1)}{2(x-1)^2}}[/tex]The result obtained can be rewritten in the form below:
[tex]=\sqrt[]{\frac{2\times6(x-1)}{2(x-1)(x-1)^{}}}[/tex]Canceling out the common factors, we have:
[tex]=\sqrt[]{\frac{6}{(x-1)^{}}}[/tex]An equivalent expression is Opt
Consider the following system of equations.ſ x - 4y = -34x - 2y = -12Step 2 of 2: Determine if the point (3, 1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Given:
x - 4y = -3
4x - 2y = -12
To determine if the point (3, 1) lies on both of the lines in the system of equations:
Substitute (3, 1) in the first equation, we get
3 - 4(1) = -3
3 - 4 =-3
-1 = -3
But,
[tex]-1\ne-3[/tex]Substitute (3, 1) in the second equation, we get
4(3) - 2(1) = -12
12 - 2 = -12
10 = -12
But,
[tex]10\ne-12[/tex]Hence, the answer is, No.
The point (3, 1) does not lie on both of the lines in the system of equations.
282The number of germs in a sample can be measured by the equation f(x)=15x + 145. Temperature represents the domain of the sample while the range isthe number of germs. If a doctor wants to keep the amount of germs to be less than 300,what is the approximate domain of temperatures to keep the sample under 300?
Answer
The approximate domain temperature is 10
Step-by-step explanation:
Given the following model function
f(x) = 15x + 145
Mathematically
15x + 145 < 300
Collect the like terms
15x < 300 - 145
15x < 155
Divide both sides by 15
15x/15 < 155/15
x < 10.33
solve by square roots: 16k^2-1=24
we have
[tex]16k^2-1=24[/tex]step 1
Adds 1 both sides
[tex]\begin{gathered} 16k^2-1+1=24+1 \\ 16k^2=25 \end{gathered}[/tex]step 2
Divide by 16 both sides
[tex]\begin{gathered} \frac{16}{16}k^2=\frac{25}{16} \\ \text{simplify} \\ k^2=\frac{25}{16} \end{gathered}[/tex]step 3
Applying square root both sides
[tex]k=\pm\frac{5}{4}[/tex]How many different arrangements of 5 be formed if the first must Work (of allowed?
ANSWER
There are 913,952 different 5-letter combinations that can be formed.
EXPLANATION
Recall that there are 26 letters in the English Alphabet.
From the question, we are to find the arrangement of 5 letters with the first letter being either W or K, and repetition of letters is allowed.
The possibilities for the 1st letter is 2 since the 1st letter can be either W or K;
More so, the possibilities for the 2nd letter is 26;
The possibilities for the 3rd letter is 26;
The possibilities for the 4th letter is 26, and
The possibilities for the 5th letter is 26;
The possibilities of arranging 5 letters = 2 x 26 x 26 x 26 x 26 = 913,952.
Hence, a total of 913,952 different 5-letter combinations can be formed.
Let p be "x+4=13" and q be "x=9." Which of the following statements is a biconditional?Select the correct answer below:x+4=13 and x=9.If x+4=13, then x=9.x+4=13 if and only if x=9.x+4=13 only if x=9.
For two given simple statements P and Q, if they are connected with the logical connectivity 'if and only if', then the compund statement is called biconditional statement.
Now,
P: x+4=13
q: x=9
Then, their biconditional statement is x+4=13 if an donly if x=9
Hence the correct answer is (c)
Khloe is going to invest $7,100 and leave it in an account for 9 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Khloe to end up with $12,600?
Solution
For this case we can use the following formula:
[tex]A=Pe^{rt}^{}[/tex]and for this case we have the following:
P= 12600
A= 7100
t = 9 years
And r is the value that we need to find, so we can do the following:
[tex]12600=7100e^{9r}[/tex]We can do the following:
[tex]\ln (\frac{12600}{7100})=9r[/tex]And we got for r:
[tex]r=\frac{\ln (\frac{12600}{7100})}{9}=0.0637[/tex]And then the rate would be:
6.37%
The figure below is an iscoceles trapezoid. If m
..Given an isosceles trapezoid
The following are the properties of an isosceles trapezoid
The legs are congruent by definition (From the diagram, the legs are JM and KL)
The lower base angles are congruent. The lower base angles are
[tex]m\angle M\cong m\angle L[/tex]The upper base angles are congruent. The upper base angles are
[tex]m\angle J\cong m\angle K[/tex]Any lower base angle is supplementary to any upper base angle. This means that
[tex]\begin{gathered} m\angle J+m\angle M=180^0 \\ m\angle K+m\angle L=180^0 \end{gathered}[/tex][tex]\begin{gathered} \text{If} \\ m\angle K=61^0 \\ \text{Therefore} \\ m\angle J\cong m\angle K=61^0 \\ m\angle J=61^0 \end{gathered}[/tex]Also,
[tex]\begin{gathered} m\angle L+m\angle K=180^0 \\ m\angle L+61^0=180^0 \\ m\angle L=180^0-61^0 \\ m\angle L=119^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle L\cong m\angle M,m\angle L=119^0 \\ Therefore\colon \\ m\angle M=119^0 \end{gathered}[/tex]Hence
m∠J = 61⁰
m∠L = 119⁰
m∠M = 119⁰
What is the opposite of the given number?-10.1
According to the given data we have the following number:
-10.1
Therefore, the opposite of this given number would be the number 10.1
Instead of -10.1 the opposite would always be with the contrary sign. In this case is the opposite is a positive number.
In this case is -10.1. but for example if we the have to find the opposite number of 1 that would be the -1.
All real number would have and opposite number, except for the number 0.
Brody spent $260 on 4 chairs. To find out how much he spent on each chair, he did the following work in long division. 65 4) 260 -24 20 -20 0 Did he do the problem correctly? Why or why not? O A. No, because there is a remainder of o. B. No, because the first digit in the quotient should be 4, not 6. O C. No, because the problem should be 260 14. O D. Yes, he worked the problem correctly.
He spend $260 on 4 chairs:
To know how much he spent on each chair he must:
Divide 260 into 4You first pick the firt digit of the dividend (260) and look if you can divide that digit into the divider (4) as in this case the firt digit 2 cannot be divided into 4 you take the first and secon digit (26) and divide it into 4 (how many times fix 4 in 26), this is equal to 6 times (this is the first digit of the quotient), then you multiply the 6 by 4 (6*4=24)and put the result under the 26 to substract it:
Now you lower the zero (of the 260) next to the result of the previous subtraction:
And divide 20 into 4 (how many times fix 4 in 20) this is equal to 5 times (this is the second digit of the quotient ) then you multiply the 5 by 4 (5/4 =20) and put the result under the 20 to substract it:
The remainder of 0 means the division has not decimal result, the result of 260 into 4 is an interger number (65)
The firt digit of the quotient is 6 because 26 into 4 is 6.
So the division he did is the correct form to find how much cost each chair ($65)Which property is used in the following calculation?
4 (18) (5)
4 (5) (18)
20 (18)
360
A. Identity Property of Multiplication
B. Distributive Property
C. None of these
D. Associative Property of Multiplication
E. Associative Property of Addition
The property which is used in the following calculation is referred to as Associative Property of Multiplication and is denoted as option D.
What is Associative Property of Multiplication?This is referred to as the process in which the the result of the multiplication of three numbers is always the same regardless of the way and manner in which they are arranged.
We were given: 4 (18) (5)
= 4 (5) (18)
= 20 (18)
= 360
The multiplication of the numbers will give the same result of 360 no matter how the numbers are arranged which is why it was chosen as the correct choice.
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Refer to attached image.
213 and 131 are incorrect.
Answer:
P(X<16) = 0.64P(X>12) = 0.64Step-by-step explanation:
Given a graph of a probability density function, you want the probabilities ...
P(X < 16)P(X > 12)Probability from PDFThe probability of a given range of values of X is the area under the density curve for those values of x.
P(X < 16)The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:
A = 1/2bh
A = 1/2(16)(0.08) = 0.64
The probability is P(X<16) = 0.64.
P(X > 12)The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...
A = 1/2(b1 +b2)h
A = 1/2(0.06 +0.10)(8) = 0.64
The probability is P(X>12) = 0.64.
please help me asap, Evaluate 9 exponent 2
81
Explanation
Remember
[tex]a^b=\text{ a multiplied by itself b times}[/tex]Step 1
apply
[tex]\begin{gathered} 9^2=9\cdot9 \\ 9\cdot9=81 \end{gathered}[/tex]Write a cosine function that has a midline of 4, an amplitude of 3 and a period of 8/5
A cosine function has the form
[tex]y=A\cdot\cos (Bx+C)+D[/tex]Where A is the amplitude, B is 2pi/T, and C is null in this case because the phase is not being specified, and D is the vertical shift (midline).
Using all the given information, we have
[tex]y=3\cdot\cos (\frac{2\pi}{T}x)+4[/tex]Then,
[tex]y=3\cdot\cos (\frac{2\pi}{\frac{8}{5}}x)+4=3\cdot\cos (\frac{10\pi}{8}x)+4=3\cdot\cos (\frac{5\pi}{4}x)+4[/tex]Hence, the function is
[tex]y=3\cos (\frac{5\pi}{4}x)+4[/tex]Hi I am the mom can you help me on this question so I can show my daughter too because I am confused
Using the area method in finding the quotient.
The values of A and B are as follows,
A = C/6
B = D/6
A is the quotient of C and 6,
B is the quotient of D and 6.
From the problem, we only have choices of number to input in the boxes.
48, 9, 90, 8, 540, 36 and 0
We will select one to number to be the value of C and the value A must be in the given numbers to be used.
Let's say C = 48
A = 48/6 = 8
Since 8 is included in the list of numbers. This is applicable.
Now for D and B,
Note that the sum of C and D must be equal to the given dividend, the dividend from the problem is 588
Since we already have the value of C = 48, the value of D must be :
588 - C = D
588 - 48 = 540
And 540 is also included in the list of numbers, so D = 540
The value of B will be :
B = D/6
B = 540/6
B = 90
90 is also included in the list of numbers.
The final diagram will be :
For part B, the quotient is the sum of A and B
A = 8, B = 90
Quotient = A + B
= 8 + 90
Quotient = 98
In a recent poll, 13% of all respondents said that they were afraid of heights. Suppose this percentage is true for allAmericans. Assume responses from different individuals are independent.
A person invested $3,700 in an account growing at a rate allowing the money to double every 6 years. How much money would be in the account after 14 years, to the nearest dollar?
Given :
The principal = 3,700
Assume a simple interest
The account growing at a rate allowing the money to double every 6 years.
So,
[tex]\begin{gathered} I=P\cdot r\cdot t \\ I=P \\ 3700=3700\cdot r\cdot6 \\ r=\frac{1}{6} \end{gathered}[/tex]How much money would be in the account after 14 years, to the nearest dollar?
So, we will substitute with r = 1/6, t = 14 years
So,
[tex]\begin{gathered} I=3700\cdot\frac{1}{6}\cdot14=8633.33 \\ \\ A=P+I=8633.33+3700=12333.33 \end{gathered}[/tex]Rounding to the nearest dollar
So, the answer will be $12,333
How many terms are included in the expression below?x² – 3x+7A. 2B. 7o oC. 1D. 3
Answer:
Choice D: 3 terms
Explanation:
The term of a expressions constant or a variable of an equation, The variable
