Solution:
Given that the area of circle Q is;
[tex]A=169\pi in^2[/tex]Also, the general formula is;
[tex]\begin{gathered} A=\pi r^2 \\ \\ \text{ Where }r=radius \end{gathered}[/tex]Thus, the radius, r, of the circle is;
[tex]\begin{gathered} 169\pi=\pi r^2 \\ \\ r^2=169 \\ \\ r=\sqrt{169} \\ \\ r=13in \end{gathered}[/tex]Thus, the diameter, d, is;
[tex]\begin{gathered} d=2r \\ \\ d=2(13in) \\ \\ d=26in \end{gathered}[/tex]ANSWER: The diameter of the circle is 26in
△ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘. What is CA ? Enter your answer rounded to the nearest tenth in the box.
The length of the side CA is 11.84cm when the triangle is ABC and the right angle is at ∠C and the length of BC is 7.7 cm and angle A is 41°.
Given that,
The triangle is ABC and the right angle is at ∠C.
The length of BC is 7.7 cm and angle A is 41°.
We have to find the length of CA.
Take the side CA as x.
Take the trigonometric ratio.
TanA =Opposite side/ adjacent side.
Tan 41° = 7.7/ x
0.65= 7.7/x
x= 7.7/0.65
x= 11.84 cm.
Therefore, The length of the side CA is 11.84cm when the triangle is ABC and the right angle is at ∠C and the length of BC is 7.7 cm and angle A is 41°.
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use basic trigonometric identities to simplify the expression: -tan (-x) cot (-x) = ?
-1
Explanation
let's remember the indentities
[tex]\begin{gathered} tan\theta=\frac{sen\text{ \lparen x\rparen}}{cos\text{ \lparen x\rparen}} \\ cot\theta=\frac{cos(x)}{sin(x)} \end{gathered}[/tex]so
Step 1
let the expression
[tex]-tan(-x)cot(-x)=?[/tex]rewrite the expression:
replace using the identity
[tex]\begin{gathered} -tan(-x)cot(-x)=? \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{cos(-x)}*\frac{cos(-x)}{\sin(-x)} \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{sin(-x)}\frac{cos\left(-x\right)}{\sin(*x)} \\ -tan(-x)cot(-x)=-1*1 \\ -tan(-x)cot(-x)=-1 \end{gathered}[/tex]therefore, the answer is
-1
I hope this helps you
A self-tanning lotion advertises that a 4-oz bottle will provide six applications. Jen found a great deal on a 19-oz bottle of the self-tanning lotion she had been using. Based on the advertising claims, how many applications of the self-tanner should Jen expect?
The number of applications of the self-tanner that Jen should expect would be= 28.5 applications
What is self-tanning lotion?A self-tanning lotion is defined as the type of lotion that can be used to artificially tan the skin and it is applied topically.
The number of applications for 4oz of the lotion= 6
The number of applications for 19oz of the lotion= X
Make X the subject of formula;
X = 19×6/4
X = 114/4
X= 28.5 applications
Therefore, based on the advertisement claims of a 19 Oz bottle of self-tanning lotion, the number of applications Jen should expect is 28.5.
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If a1=2 and an+1 =(an)² - 4 then find the value of a4
From the Question given, we are able to write the following relationship:
[tex]\begin{gathered} a_1=2 \\ a_{n+1}=(a_n)²-4 \end{gathered}[/tex]By substituting the values 1, 2, and 3, we are able to calculate as follows:
[tex][/tex]I need help with this question... the correct answer choice
Given:
P(2,-4) to point P'(-2,1)
[tex]P(2-4,-4+5)=P^{\prime}(-2,1)[/tex][tex](x,y)\rightarrow(x-4,y+5)[/tex]3rd option is the correct answer.
Please help me with #1Please help me on my hw
The given expression is,
[tex](2x^2)^3[/tex]According to the law of exponents,
[tex]\begin{gathered} (xy)^m=x^my^m\text{ ---(a)} \\ (x^m)^n=x^{mn}\text{ ---(b)} \end{gathered}[/tex]Applying the law of exponents to the given expression,
[tex]\begin{gathered} (2x^2)^3=2^3(x^2)^3\text{ (using law (a))} \\ =8x^{2\times3}\text{ (using law (b))} \\ =8x^6 \end{gathered}[/tex]Therefore, the correct expression is
[tex](2x^2)^3=8x^6[/tex]
Describe how the graph of the function is a transformation of the original function f.y=f(x+16)This results in a Answer shift to the graph Answer units Answer.
When we add a constant to the argument of a function, we are shifting the graph horizontally. If the constant is positive, the graph gets shifted to the left, if it's negative, the graph gets shifted to the right.
With this in mind we can solve the problem. The constant "16" was added to the argument of the function "f(x)". This results in a "horizontal" shift to the graph "16" units "to the left".
Two fifths of the instruments in the marching band are brass
A 4/15 fraction of the band's instruments are woodwinds.
What is a fraction?It describes how many parts of a certain there are. The foundations of fractions explain the top and bottom numbers in a fraction. It represents a numerical value that expresses a part of a whole. The whole can be any specific value or a particular number. A fraction has two parts. The figure above the line is known as the numerator and the number below the line is termed the denominator.
Given, two-fifths of the marching band is brass. And one-third of them are percussion.
Multiply 2/5 by 3 we get, 6/15
And multiply 1/3 by 5 we get, 5/15
Given, that the rest are woodwind instruments,
Then, 1-(6/15)-(5/15)=4/15
4/15 fraction of the band's instruments are woodwinds
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The complete question is:
"Two-fifths of the instruments in the marching band are brass, one-third are percussion, and the rest are woodwinds. What fraction of the band is woodwinds?"
A sun is a distant of galaxy what is the distance
We would divide the mass of the sun by the mass of the earth. From the information given,
mass of earth = 5.972 x 10^24
mass of sun = 1.61244 x 10^31
Number of earths = 1.61244 x 10^31/5.972 x 10^24 = 2.7 x 10^6
It will take 2.7 x 10^6 to equal the mass of the sun
Use quadratic formula to find the roots of x^2+2x-7
Okay, here we have this:
[tex]x^2+2x-7=0[/tex]We will solve using the general formula, then we obtain:
[tex]\begin{gathered} x_{1,2}=\frac{-2\pm\sqrt[]{2^2-4\cdot1\cdot(-7)}}{2\cdot1} \\ =\frac{-2\pm\sqrt[]{4+28}}{2} \\ =\frac{-2\pm\sqrt[]{32}}{2} \\ =\frac{-2\pm4\sqrt[]{2}}{2} \end{gathered}[/tex]Let's separate the solutions:
[tex]\begin{gathered} x_1=\frac{-2+4\sqrt[]{2}}{2} \\ =\frac{2(-1+2\sqrt[]{2})}{2} \\ =-1+2\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} x_2_{}=\frac{-2-4\sqrt[]{2}}{2} \\ =\frac{2(-1-2\sqrt[]{2})}{2} \\ =-1-2\sqrt[]{2} \end{gathered}[/tex]Finally we obtain that the roots are: -1+2√2 and -1-2√2.
2) Joe has a cube of cheese that measures 4 inches on each edge. He cuts out a 1-inch cube of
cheese from each of the eight corners, as shown below. What percentage of the cheese does
Joe cut out from the original cube of cheese? Express your answer as a decimal.
The percentage of the cheese cut off by Joe from the original cube of cheese is 12.5% by application of the formula for finding the volume of a cube.
Volume of a cubeThe volume of a cube is defined as the total number of cubic units occupied by the cube. The formula is given as V = a³ where "a" is the length of edge or sides.
Given that the cube of cheese has 4inches of length on its edges, then volume;
V = 4³inches
V = (4×4×4) inches
V = 64inches
the total volume cut off by Joe from the original cube of cheese;
V = 1inch × 8edges of the cube cheese
V = 8inches
Therefore, the percentage of the cube cheese cut off by Joe from the original cheese is derived as;
(8/64) × 100 = 12.5% by simplification.
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The graph of a function is shown on the coordinate plane below. Which relationship represents a function with the same slope as the function graphed?
If (x_1, y_1) and (x_2, y_2) are points of a line, its slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]From the graph of the function, we see that the line passes through the points:
• (x_1, y_1) = (-1, 6),
,• (x_2, y_2) = (0, 1).
The slope of the line is:
[tex]m=\frac{1-6}{0-(-1)}=-5.[/tex]A) Using the points:
• (x_1, y_1) = (-2, 0),
,• (x_2, y_2) = (2, 10).
We find that the slope of this line is:
[tex]m=\frac{10-0}{2-(-2)}=\frac{10}{4}=2.5.[/tex]This function has not the same slope as the line of the graph.
B) The general equation of a line is:
[tex]y=m\cdot x+b\text{.}[/tex]Where m is the slope and b is the y-intercept.
Comparing the general equation with the equation:
[tex]y=-5x+3,[/tex]we see that the slope of the line of this equation is m = -5.
This function has the same slope as the line of the graph.
C) Using the points:
• (x_1, y_1) = (-4, 8),
,• (x_2, y_2) = (0, 5).
We find that the slope of this line is:
[tex]m=\frac{5-8}{0-(-4)}=-\frac{3}{4}=-0.75.[/tex]This function has not the same slope as the line of the graph.
D) Comparing the general equation with the equation:
[tex]y=-\frac{5}{4}x+2.[/tex]we see that the slope of the line of this equation is m = -5/4.
This function has not the same slope as the line of the graph.
Answer
B. y = -5x + 3
Find the circumference of a circle with an area of 95.03 m^2. Round the answer to the nearest tenth.
The area of a circle with radius r is given by the following formula:
[tex]A=\pi r^2[/tex]The circumference of that circle is given by:
[tex]C=2\pi r[/tex]Finding the answerWe are given the area of the circle. With this data and the first formula we can construct an equation for the radius r. Once we find the radius of the circle we can use it to find its circumference. So first of all we take the first formula and we equalize it to 95.03:
[tex]95.03=\pi r^2[/tex]We can divide both sides by π:
[tex]\begin{gathered} \frac{95.03}{\pi}=\frac{\pi r^2}{\pi} \\ r^2=\frac{95.03}{\pi} \end{gathered}[/tex]Now we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{r^2}=\sqrt{\frac{95.03}{\pi}} \\ r=\sqrt{\frac{95.03}{\pi}} \end{gathered}[/tex]And that's the radius of the circle. Then we can use this value in the formula of the circumference C:
[tex]C=2\pi *\sqrt{\frac{95.03}{\pi}}=34.6[/tex]AnswerThen the answer is 34.6 m.
x^2- 20x = -2x – 80In (x+a)^2=b form please hurry
Completing Squares
It's given the following equation:
[tex]x^2-20x=-2x-80[/tex]We are required to express the equation in the form:
[tex](x+a)^2=b[/tex]The first step is sending all the variables to the left side of the equation.
Adding 2x:
[tex]\begin{gathered} x^2-20x+2x=-80 \\ \\ \text{Simplifying:} \\ x^2-18x=-80 \end{gathered}[/tex]To complete squares, we need to recall the following identity:
[tex]p^2+2pq+q^2=(p+q)^2[/tex]The expression on the left side is missing the third term to be a perfect square. Note that comparing
p=x
2pq = -18x
This means that
q = -18x/2p
q = -18x/2x
q = -9
Now we know the value of the second term, we need to add q^2=81:
[tex]x^2-18x+81=-80+81[/tex]The left side of the equation is the square of x-9, and the right side can be calculated:
[tex](x-9)^2=1[/tex]Now we have the required expression, where a=-9 and b = 1
-------------------
9Philip is saving money to buy a new computer. He saves the same amount ofmoney each week.After 2 weeks of saving, Philip still needs $520 to buy the computer.After 6 weeks of saving, Philip still needs $300 to buy the computer.How much does the computer cost?
First let's calculate how much money Philip saves each week.
In 4 weeks, he saved 520 - 300 = $220, so he saved 220/4 = $55 per week.
Then, we have that after 2 weeks of saving, he still needed $520, so before this saving, he needed:
[tex]\begin{gathered} 520+2\cdot55 \\ =520+110 \\ =630 \end{gathered}[/tex]So the computer costs $630.
1/2 to 3rd power1/2 to the 3rd power
Let's begin by identifying key information given to us:
[tex]\begin{gathered} (\frac{1}{2})^3=\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{8} \\ \Rightarrow(\frac{1}{2})^3=\frac{1}{8} \end{gathered}[/tex]How do I solve the role of zero?f(x) = (x - 2)^5 (x + 4)^3
ANSWER
2 and -4
EXPLANATION
We are given the function:
f(x) = (x - 2)^5 (x + 4)^3
We simply need to find the zeros of the function and to do that, we need to find the values of x such that the function will be 0.
The function has already been factorised and so, we simply need to identify the zeros.
There are two zeros for the function and they are 2 and -4.
This is because when x is either 2 or -4, the function resolves to 0.
When x = 2:
[tex](2-2)^5(2+4)^3=0(6)^3\text{ = 0}[/tex]and when x = -4:
[tex](-4-2)^5(-4+4)^3=(-6)^50\text{ = 0}[/tex]And so, the zeros of the function are 2 and -4.
At a party, there are 40 prizes, which are either kazoos or whistles. The tape diagram shows the ratio of kazoos to whistles.
kazoos: 3-15
whistles: 5-25
Total Prizes: 8-40
Khan Academy
Using ratios we know that there are 15 kazoos and 25 whistles out of the total 40 gifts.
What are ratios?In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons. Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.So, the complete number of prizes—is 40 kazoos or whistles.
The ratio of whistles to kazoos is shown in the diagram.The original proportion of kazoos to whistles was therefore 3:5.Using this ratio, the total prize equals 3 + 5 = 8.Assume that there are 3 times as many Kazoos.Whistles = number of times 5We can state that 3/8 of the total rewards will be kazoos and 5/8 of the total awards will be whistling in this case.
Quantity of kazoos: 3/8 × 40 = 15The quantity of whistling: 5/8 × 40 = 25Therefore, using ratios we know that there are 15 kazoos and 25 whistles out of the total 40 gifts.
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4(3y-7)=-3(-2y) - 4
What is the y
Answer:
y=4
Step-by-step explanation:
first we have to distribute
4(3y)+(4)(-7)=-3(-2y)-4
12y-28=6y-4
6y-28=-4
6y=24
y=4
Hopes this helps please mark brainliest
A student cafeteria has 24 tables, tables X has 4 seats each, tables Y has 6 seats each, and tables Z has 10 seats each. The total seating capacity of the cafeteria is 148. For a student meeting, half of tables X, 1/4 of tables Y, and 1/3 of tables Z will be used, for a total of 9 tables. Determine X, Y, and Z. ( Answer the final answer in a full sentence. )
Answer: For a meeting, half of x, 1/4 of y, and 1/3 of z will be used for a total of 9 tables:
[tex]\begin{gathered} x+y+z=9 \\ \\ \\ \\ \frac{1}{2}x=\frac{4}{2}=2 \\ \\ \frac{1}{4}y=\frac{6}{4}=\frac{3}{2} \\ \\ \frac{1}{3}z=\frac{10}{3} \\ \\ \text{ Since we have a total of 9 tables therefore we have:} \\ \\ 3x+3y+3z\Rightarrow\text{ Total number of chairs.} \\ \\ 3(2)+3(\frac{3}{2})+3(\frac{10}{3})=6+\frac{9}{2}+10 \\ \\ \\ \text{Therefore:} \\ \\ ------------------------------- \\ \\ x=6 \\ \\ y=\frac{9}{2} \\ \\ z=10 \end{gathered}[/tex]Therefore the x = 6 and y = 9/2 and z = 10 is the answer.
An employee makes $10.51 per hour but is getting a 3% increase. What is his new wage per hour to the nearest cent?
First, we find 3% of $10.51.
[tex]0.03\cdot10.51=0.32[/tex]Then, we add this increase to $10.51.
[tex]10.51+0.32=10.83[/tex]Hence, the new wage per hour is $10.83.If a savings account of $19,400 is compounded semiannually at 5,07% annual interest, how much will the account be worth in 32 months? Round your answer to thenearest cent, if necessary. Note: 365 days in a year and 30 days in a month.
From the question, we are provided with the following information:
[tex]\begin{gathered} \text{Principal, P=\$19,400} \\ \text{Rate, r=5.07\%} \\ r=\frac{5.07}{100}=0.0507 \\ \text{Time, t(in years)=}\frac{32}{12}=2.67years \\ N\text{umber of times interest applied per time period, n=2(semi-annually)} \end{gathered}[/tex]The required parameter we are to find is the Amount, A.
Amount of a compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Thus, we have:
[tex]\begin{gathered} A=19,400(1+\frac{0.0507}{2})^{2\times2.67} \\ A=19400(1+0.02535)^{5.34} \\ A=19400(1.02535)^{5.34} \\ A=19400\times1.143 \\ A=\text{ \$22,174.76} \end{gathered}[/tex]Hence, the account will be worth $22,174.76 in 32 months
Mr. Abraham, a married man, works a 40 hour work week, 48 wooks each yoor, His hourly rate of pay is $36.60 por hour. Aftor tax deductions for his two exemptions, his bl-wookly taxablo wagos were 12,410.77. How much is deducted from each paycheck for fodoral income tax? Noto: Porcontage mothod for calculation: For taxablo bi-wooklywages over 5066, but not over $2,698 - 366,40, plus 18% of excess over $068.$200,00$278.56$283.32$294.70None of these choices are correct.
We know that the biweekly tax is equal to $65.40 plus 15% of excess over $958. In this case the excess is:
[tex]2410.77-958=1452.77[/tex]Then for this excess the tax is:
[tex]0.15\cdot1452.77=217.92[/tex]Hence the total tax is:
[tex]217.92+65.40=283.32[/tex]Therefore the answer is the third option.
1,1,2,2,2,5,5,8,9,10,11
In order to calculate the median the data should be arranged in order from least to greatest.
According to this question we have the following number:
1,1,2,2,2,5,5,8,9,10,11
So, we would proceed to arrange the number as follows:
1, 1, 2, 2, 2, 5, 5, 8, 9, 10, 11
As we have a total of number of 11, then that means that the median would be the central score of it.
Therefore, in this case the central score
Which of the following transformations accurately describes the relationship between the two trapezoids?A. Dilate the blue trapezoid by a scale factor of ½ to obtain the red trapezoid.B. Dilate the red trapezoid by a scale factor of 2 to obtain the blue trapezoid.C. Dilate the red trapezoid by a scale factor of ½ to obtain the blue trapezoid.D. Dilate the blue trapezoid by a scale factor of 3 to obtain the red trapezoid.
Given: Two trapezoid as shown in the image
To Determine: The transformation that relates the two trapezoids
Solution
Let us determine the coordinates of the two trapezoid as shown below
We can relate the blue trapezoid to the red trapezoid
[tex]\begin{gathered} (3,1.5)\rightarrow(6,3) \\ (4.5,1.5)\rightarrow(9,3) \\ (3,3)\rightarrow(6,6) \\ (4.5,4.5)\rightarrow(9,9) \end{gathered}[/tex]It can be observed that the transformation rule that relates the blue trapezoid to the red trapezoid is
[tex](x,y)\rightarrow(2x,2y)[/tex]It can be observed that the blue trapezoid is enlarged by a scale factor to get the red trapezoid. So, we dilate the blue trapzoid by a scale factor of 2 to get the red trapezoid.
From the options provided, the best answer related the red trapezoid to the blue trapezoid, which is a reduction by a scale factor of 1/2
Hence, the correct option is
Dilate the red trapezoid by a scale factor of 1/2 to obtain the blue trapezoid, OPTION C
jon: 1 ptgiven by f(x) = |x| – 4. Find each of the indicated function values.(b) f(4)(c) f(a + 4)(Simplify your answer.)
we have
f(x) = |x| – 4
Part b
f(4)
so
For x=4
substitute in the expression above
f(4) = |4| – 4
f(4)=4-4
f(4)=0
Part c
f(a+4)
so
For x=(a+4)
substitute
f(a+4) = |(a+4)| – 4
f(a+4)=a+4-4
f(a+4)=a
Convert the repeated decimal 0.47 into a fraction using infinite geometric series.
Answer:
47/99
Explanation:
Given the repeated decimal 0.4747...
This can be splitted into;
0.47 + 0.0047 + 0.000047 + ...
On rewriting;
47/100 + 47/10000 + 47/1000000 + ...
The given series is a geometric progression
The sum to infinity of a geometric progression is expressed as;
[tex]S\infty\text{ = }\frac{a}{1-r}[/tex]a is the first term
r is the common ratio
From the sequence;
a = 47/100
r = (47/10000)/(47/100)
r = 47/10000 * 100/47
r = 1/100
Substitute;
[tex]\begin{gathered} S\infty\text{ = }\frac{\frac{47}{100}}{1-\frac{1}{100}} \\ S\infty\text{ = }\frac{\frac{47}{100}}{\frac{99}{100}} \\ S\infty\text{ = }\frac{47}{100}\cdot\frac{100}{99} \\ S\infty\text{ = }\frac{47}{99} \end{gathered}[/tex]Henec the repeated fraction to decimal is 47/99
Which ratio represents the ratio 6 cups to 4 quarts in simplest form? ●3 to 8 ●6 to 16 ●3 to 4 ●3 to 2
Simplift the ratio of 6 cups to 4 quarts.
[tex]\begin{gathered} \frac{6}{4}=\frac{2\times3}{2\times2} \\ =\frac{3}{2} \end{gathered}[/tex]So in simplest form ratio is 3 to 2.
Estimate the sum of the decimals below by rounding to the nearest whole number. Enter your answer in the space provided gym
Given:
[tex]5.029,8.315,5.284[/tex]Required:
Find the estimated sum of the given decimals to the nearest whole number.
Explanation:
The estimated sum by rounding to the nearest whole number is 19.
Final Answer:
The estimated sum of the given decimals by rounding to the nearest whole number is 19.
Supposed that the mean systolic blood pressure for women I’ve age seventy is 131mmHg ( millimeters of mercury), with a standard deviation of 9 mmHg. Supposed that the blood pressure are normally distributed. Complete the following statements ( choose correct answers 68%,75%,95%,99.7%)
To answer the question, having a z-table with you will help. We can also use the 68-95-99.7 rule.
The rule states that 68.27% of a normally distributed data set is within one standard deviation of the mean, 95.45% is within two standard deviations, and 99.73% is with three standard deviations.
Given that the mean is 131 mmHg and the standard deviation is 9 mmHg, we can calculate the boundaries which are 3 standard deviations away from the mean by adding and subtracting three times the standard deviation.
[tex]\begin{gathered} 131-(3\times9)=104 \\ \\ 131+(3\times9)=158 \end{gathered}[/tex]Therefore, approximately 99.7% of women over seventy have blood pressures between 104 mmHg and 158 mmHg.
Now let's find out how many standard deviations away 122 mmHg and 140 mmHg are from the mean.
[tex]\begin{gathered} z=\frac{122-131}{9}=-1 \\ \\ z=\frac{140-131}{9}=1 \end{gathered}[/tex]122 and 140 mmHg are within 1 standard deviation of the mean. Using the 68-95-99.7 rule, we know that approximately 68.27% of women over seventy have blood pressures between 122 mmHg and 140 mmHg.