a)
The expression given is:
[tex]\frac{5(x+7)}{3}[/tex]From this we can see that:
7 is added to a number, x
Then the whole thing is multiplied by 5 as shown by the parenthesis around it
Then the whole thing is divided by 3
So, the steps would be:
• Add 7 to the number
,• Multiply by 5
,• Divide by 3
b)
In order to simplify, we firsst distribute the 5:
[tex]\begin{gathered} \frac{5(x+7)}{3} \\ =\frac{5x+35}{3} \end{gathered}[/tex]This can be the final form, or we can divide the two terms by 3 and leave it added together:
[tex]\begin{gathered} \frac{5x+35}{3} \\ =\frac{5x}{3}+\frac{35}{3} \end{gathered}[/tex]please show me how to use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1 if you can, I have the steps already but I'm struggling to understand still.
Power reduction formulas for squares:
[tex]\begin{gathered} \sin ^2u=\frac{1-\cos (2u)}{2} \\ \\ \cos ^2u=\frac{1+\cos (2u)}{2} \end{gathered}[/tex]Given expression:
[tex]72\sin ^2x\cos ^2x[/tex]Use the reduction formula: For the given expression u is x:
[tex]=72\cdot\frac{1-\cos2x}{2}\cdot\frac{1+\cos2x}{2}[/tex]Simplify:
-Multiply:
[tex]=\frac{72\cdot(1-\cos 2x)(1+\cos 2x)}{4}[/tex]-Divide 72 into 4:
[tex]=18(1-\cos 2x)(1+\cos 2x)[/tex]Then, an equivalent expression that does not contain powers of trigonometric functions greater than 1 is:
[tex]18(1-\cos 2x)(x+\cos 2x)[/tex]susie’s hair is sixteen inches long and it grows 2 inches in length (L) every three months (m) i’m wondering how to get the linear table and what the initial value is
Okay, here we have this:
We can observe that the y-intercept (when m = 0) is equal to 16 inches, and that the slope is 2/3, therefore we obtain the following equation:
L(m)=2/3m+16
Graph the points in the figure below, and find the perimeter of each shape. Round to the nearest tenth if necessary. (1,-4), (3,-4), (4, -3), (1, -2)
graphing
to find the perimeter we need the measure of each side
we can use the formula to find the distance
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]where (x1,y1) and (x2,y2) are the coordinates of each point
Side AB
[tex]\begin{gathered} \sqrt[]{(1-4)^2+((-2)-(-3))^2} \\ \\ \sqrt[]{-3^2+1^2} \\ \\ AB=\sqrt[]{10} \end{gathered}[/tex]Side BC
[tex]\begin{gathered} \sqrt[]{(4-3)^2+((-3)-(-4))^2} \\ \\ \sqrt[]{1^2+1^2} \\ \\ BC=\sqrt[]{2} \end{gathered}[/tex]Side CD
[tex]\begin{gathered} \sqrt[]{(3-1)^2+((-4)-(-4))^2} \\ \\ \sqrt[]{2^2+0^2} \\ \\ CD=2 \end{gathered}[/tex]Side DA
[tex]\begin{gathered} \sqrt[]{(1-1)^2+((-4)-(-2))^2} \\ \\ \sqrt[]{0^2+(-2)^2} \\ \\ DA=2 \end{gathered}[/tex]now, sum the sides
[tex]\begin{gathered} P=AB+BC+CD+DA \\ P=\sqrt[]{10}+\sqrt[]{2}+2+2 \\ P=8.576 \end{gathered}[/tex]rounding the perimeter is 8.6 units
for each set points a and b below use a straight edge to draw the indicated geometric object
In this case the answer is very simple.
You must use a ruler to draw the corresponding ray.
In part a) the ray is BA.
In part b) and c) you must do the same by joining both points by a straight line.
That is the solution.
Which of the following is the best definition of like radical terms? A. Terms that have different degrees and different radicands B. Terms that have the same degree and the same radicand O C. Terms that have the same degree but different radicands D. Terms that have different degrees but the same radicand
we know that
Radicals with the same index and radicand are known as like radicals
therefore
The answer is option BWhat is the measure of an angle that turns through 3/8 of a circle?
The total angle in a circle is 360°.
Therefore, the measure of an angle that turns through 3/8 of a circle is
[tex]\frac{3}{8}of360^0[/tex]Evaluate the above
[tex]\frac{3}{8}\times360^0=3\times45^0=135^0[/tex]Hence, the answer is
[tex]135^0[/tex]Sun lei bought a laptop computer for $1500. The total cost, including tax, came $1590. What is the tax rate?
We know that Sun lei bought a laptop computer for $1500 and the total cost, including tax, came $1590.
And we must find the tax rate.
If the total cost was $1590 and the laptop cost was $1500, then the cost of the tax is
[tex]\text{tax}=1590-1500=90[/tex]Now, We must find what percentage represents $ 90 within $ 1500 and that will be the tax rate
[tex]\text{ tax rate}=\frac{90}{1500}\cdot100\text{ \%}=0.06\cdot100\text{ \%}=6\text{ \%}[/tex]Finally, the tax rate is 6%
[tex]8.093 + 11.92 [/tex]add 8.093+11.92
We have to add 8.093+11.92.
To add the decimal numbers, write down the numbers one below the other in such a way that decimals are aligned.
Put zeros so that the number of digits is same in both numbers.
The rounded numbers are remainders.
So, the result of 8.093+11.92 is 20.013
<1Point P is shown on the number line below.PHHHHHH0 2. 4 6-12-10 -8 -6 -4 -2810 121The distance between point Q and point P is 6 units. Which number could represent point Q?2А0 101
Explanation:
If the distance between point Q and point P is 6 1/2 units, Q can be 6 1/2 units to the right of P or Q can be 6 1/2 units to the left of P.
So, we will find both options and compare them to the answer options to know which one is correct.
If Q is 6 1/2 units to the right of P, we can find Q adding 6 1/2 to the coordinate of P, so the coordinate for Q, in this case, will be:
[tex]Q=P+6\frac{1}{2}=-4+6+\frac{1}{2}=2+\frac{1}{2}=2\frac{1}{2}[/tex]Remember that 6 1/2 is equivalent to 6 + 1/2 and 2 + 1/2 is equivalent to 2 1/2.
In the same way, if Q is 6 1/2 units to the left of P, we need to subtract 6 1/2 to the coordinate of P. So, the coordinate of Q can also be:
[tex]undefined[/tex]what is the common difference of the associated arithmetic sequence?
We are asked to find the common difference of associated arithmetic sequence.
The common difference is basically the difference between any two consecutive terms.
d = 70 - 54 = 16
d = 54 - 38 = 16
d = 38 - 22 = 16
d = 22 - 6 = 16
As you can see, the common difference is 16 and is the same between any two consecutive terms
Therefore, for the given arithmetic sequence, the common difference is 16.
Students are selling tickets for a school fundraiser. they collect $24 for every 10 raffle tickets they sell.2. Label and scale the axes and graph this situation with M on the vertical axis and R on the horizontal axis. Make sure the scale is large enough to see how much they would raise if they sell 1000 tickets. The scale should be___for the x-axis and____for the y-axis.
label the graph as having positive correlation negative correlation or no correlation
Given the variables y and x
If these variables have a negative linear correlation, the slope of the graphic (correlation coefficient) will be negative:
ρ<0
If the variables x and y have a positive linear correlation, the slope of the graphic will be positive:
ρ>0
If the variables x and y have are not correlated, the slope of the graphic will be zero:
ρ=0
For the given graph, the variable y increases together with the variable x, the slope of the graph is positive.
So you can conclude that there is a positive correlation between these two variables.
for the bridge shown, if the top is 30 feet long, the bottom is 40 feet long, and the bridge has a height of 15 feet, what is the area of the side of the bridge?
Bridge area= Triangle + Rectangle
. = (1/2)15• (40-30) + 30• 15
. = 150/2
Then answer is
Bridge a
.
i missed class yesterday. we have an assignment to do. i don’t understand and need help.
The given system is:
[tex]\begin{gathered} 8x+11y=37 \\ 8x+y=7 \end{gathered}[/tex]Notice that the coefficients of x in both equations are the same.
Therefore, Subtract the first equation form the second to eliminate the variable x:
[tex]\begin{gathered} 8x-8x+11y-y=37-7 \\ 10y=30 \\ y=\frac{30}{10}=3 \end{gathered}[/tex]
Substitute y = 3 into the second equation:
[tex]\begin{gathered} 8x+3=7 \\ 8x=7-3=4 \\ x=\frac{4}{8}=\frac{1}{2} \end{gathered}[/tex]Hence, the solution of the system is:
x = 1/2 and y = 3
(Statistics) answer part A, B, and C of the question in 1-3 complete sentences each.
Mean is 0.45
Standard deviation: 0.07
c) Z=p-hat-p/√(p(1-p)/n)
Z=0.40-0.45/√(0.45*0.55)/50
Z=0.40-0.45/0.07
Z=-0.71
P(p-hat≤0.40)=P(Z≤-0.71)=0.239
The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough.
How large is "large enough"? The answer depends on two factors.
Requirements for accuracy. The more closely the sampling distribution needs to resemble a normal distribution, the more sample points will be required.
The shape of the underlying population. The more closely the original population resembles a normal distribution, the fewer sample points will be required.
Use the product-to-sum identities to rewrite the following expression as a sum or difference.Зл3sin () cos (35)5л2COS2
Answer:
The expression is given below as
[tex]3\sin (\frac{5\pi}{2})\cos (\frac{3\pi}{2})[/tex]Concept:
The product to sum identity to be used is given below as
[tex]\begin{gathered} \sin A\cos B=\frac{1}{2}(\sin (A+B)+\sin (A-B) \\ A=\frac{5\pi}{2},B=\frac{3\pi}{2} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} 3\sin (\frac{5\pi}{2})\cos (\frac{3\pi}{2})=3\times\frac{1}{2}(\sin (\frac{5\pi}{2}+\frac{3\pi}{2})+\sin (\frac{5\pi}{2}-\frac{3\pi}{2}) \\ 3\sin (\frac{5\pi}{2})\cos (\frac{3\pi}{2})=\frac{3}{2}(\sin (\frac{5\pi+3\pi}{2})+\sin (\frac{5\pi-3\pi}{2}) \\ 3\sin (\frac{5\pi}{2})\cos (\frac{3\pi}{2})=\frac{3}{2}(\sin (\frac{8\pi}{2})+\sin (\frac{2\pi}{2}) \\ 3\sin (\frac{5\pi}{2})\cos (\frac{3\pi}{2})=\frac{3}{2}(\sin (\frac{8\pi}{2})+\sin (\frac{2\pi}{2}) \\ 3\sin (\frac{5\pi}{2})\cos (\frac{3\pi}{2})=\frac{3}{2}(\sin (4\pi)+\sin (\pi) \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow\frac{3}{2}(\sin (4\pi)+\sin (\pi)[/tex]A town has a population of 1.239 x 10' and shrinks at a rate of 9.4% every year.Which equation represents the town's population after 7 years?Submit AnswerO P = (1.239 x 105)(1 – 0.094)?OP= (1.239 x 10")(1+0.094)7O P = (1.239 x 10")(1.094)?O P = (1.239 x 105)(0.06)?
ANSWER:
[tex]P=(1.239\operatorname{\times}10^5)(1-0.094)^7[/tex]STEP-BY-STEP EXPLANATION:
An exponential equation has the following general form:
[tex]y=A\cdot(1\pm r)^x[/tex]Where A is the initial value and r is the rate of change.
In this case the value is 1.239 x 10^5 and r is equal to -9.4%, also x is equal to 7, since it is 7 years later.
Therefore, the equation would be:
[tex]\begin{gathered} P=(1.239\times10^5)(1-9.4\operatorname{\%})^7 \\ \\ P=(1.239\times10^5)(1-0.094)^7 \end{gathered}[/tex]Therefore, the correct answer is the 1st option.
Answer: P=(1.239 x 10*5)(1 - 0.094)*7
I am going to take a picture of the question as you can see the question has already been answered my teacher wants me to show how she got the answer.
The surface area of a sphere is given by the equation;
[tex]4\pi r^2[/tex]The ratio of the surface areas of the two spheres can be expressed as;
[tex]\begin{gathered} 4\pi r^2_1\colon4\pi r^2_2\text{ = 1:16} \\ \text{The equation becomes:} \\ \\ r^{2\text{ }}_1\colon r^2_2\text{ = 1:16 (The 4}\pi s\text{ cancel out each other)} \\ \text{The equation above implies;} \\ r^2_1\text{ = 1 }\Rightarrow r_1=1 \\ r^2_2\text{ = 16 }\Rightarrow r_2\text{ = 4} \end{gathered}[/tex]The volume of a sphere is given by the equation:
[tex]V\text{ = }\frac{4}{3}\pi r^3^{}[/tex][tex]\begin{gathered} \text{For r}_1\text{ = 1} \\ V_1=\text{ }\frac{4}{3}\text{ x }\pi x1^{3\text{ }}\text{ }\Rightarrow\text{ }\frac{4}{3}\pi \\ \\ \text{For r}_2\text{ = 4} \\ V_2=\frac{4}{3}_{}\text{ x }\pi x4^3 \\ \\ V_1\colon V_2\text{ = }\frac{4}{3}\pi\text{ : }\frac{4}{3}\pi x4^3 \\ (\frac{4}{3}\pi\text{ will cancel out each other)} \\ \\ We\text{ will be left with the equation:} \\ V_1\colon V_2=1\colon4^3\text{ }\Rightarrow\text{ 1:64} \end{gathered}[/tex]Luis made the arrays shown at the right to find 5 x 8. explain how he could change the arrays to find 7 x 8. Add to Luis's drawing to show your solution
Answer:
Step-by-step explanation:
A raffle has 250 tickets. One ticket will win a $460 prize. The rest will win nothing. X is the payoff for one ticket in the raffle. Write the probability distribution of X in the table below. Write each probability as an exact decimal. Х P(X)
Let X be the payoff for one ticket in the raffle. This variable has two possible outcomes, that the ticket is a winning ticket, in this case, you will win $460, or that the ticket has no price, then the profit will be $0.
To determine the probability of each outcome, you have to divide the number of favorable outcomes (nº of tickets that have/have not prize) by the total number of tickets of the raffle.
The raffle has 250 tickets
1 ticket has a $460 prize
249 tickets have no prize
The corresponding probabilities for both outcomes can be calculated as follows:
[tex]P(460)=\frac{1}{250}=0.004[/tex][tex]P(0)=\frac{249}{250}=0.996[/tex]You can arrange the possible values of X and their corresponding probabilities P(X) as follows:
For each ordered pair (x, y), determine whether it is a solution to the inequality 6x + 5y > 2.
Okay, here we have this:
Considering the provided inequality, and the provided ordered pairs, we are going to check it, replacing one by one in the inequality, in case the inequality is fulfilled then they are solution, otherwise it will not be, so we obtain the following:
(2, 0):
6x + 5y > 2
6(2)+5(0)>2
12+0>2
12>0
Since the inequality holds, then the ordered pair is a solution.
(7, -8):
6x + 5y > 2
6(7)+5(-8) > 2
42-40>2
2>2
Since the inequality is not satisfied, then the ordered pair is not a solution.
(3, 2):
6x + 5y > 2
6(3)+5(2) >2
18+10>2
28>2
Since the inequality holds, then the ordered pair is a solution.
(-8, 6):
6x + 5y > 2
6(-8)+5(6) >2
-48 + 30 > 2
-18 > 2
Since the inequality is not satisfied, then the ordered pair is not a solution.
The endpoints of the diameter of a circle are (2, 2) and (-4,-2). Sketch the circle. a. What are the coordinates of the center of the circle? b. What is the measure of the radius of the circle? c. Find the area and circumference of the circle to the nearest tenth.
a.
b. Let's find the diameter using the distance formula:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where:
(x1,y1) = (2,2)
(x2,y2) = (-4,-2)
[tex]\begin{gathered} d=\sqrt[]{(-4-2)^2+(-2-2)^2} \\ d=\sqrt[]{(-6)^2+(-4)^2} \\ d=\sqrt[]{52} \\ d=2\sqrt[]{13}\approx7.2111 \end{gathered}[/tex]The radius of the circle is the diameter of the circle divided by 2:
[tex]r=\frac{d}{2}=\sqrt[]{13}\approx3.6[/tex]c. The area is given by:
[tex]A=\pi\cdot r^2=\pi\cdot(\sqrt[]{13})^2=\pi\cdot13\approx40.8[/tex]And the circumference is given by:
[tex]C=2\cdot\pi\cdot r=2\cdot\pi\cdot\sqrt[]{13}\approx22.6[/tex]=O EQUATIONS AND INEQUALITIESTranslating a phrase into a one-step expressionTranslate the phrase into an algebraic expression.b times 5+ローロロメロローロDOo ?
Answer: We need to translate the phrase "b times 5" Into algebraic expression, the algebraic expression is as follows:
[tex]5b\Rightarrow\text{ Five b or b times five}[/tex]-0.25z = -1.25z=??[tex] - 0.25z = - 1.25 \\ \\ z = [/tex]
Answer:
z = 5
Explanation:
Given the below equation;
[tex]-0.25z=-1.25[/tex]To find z, all we need to do is divide both sides of the equation by -0.25;
[tex]\begin{gathered} \frac{-0.25z}{-0.25}=\frac{-1.25}{-0.25} \\ \therefore z=5 \end{gathered}[/tex]Frank is an architect. He wants to make a circular tile mosaic with a distinct border on the floor of the lobby. He lays out the mosaic design to have a diameter of 1,220 millimeters and finds the circumference to be approximately 3,830.8 millimeters as shown below.What can Frank do to improve the accuracy of measurement of the circumference? A. Use diameter instead of radius to find circumference. B. Remeasure the radius using meters. C. Remeasure the radius using a yard stick. D. Use 3.14159 for π .
Answer:
D. Use 3.14159 for π.
Explanation:
Given a circle with diameter, d, the circumference is calculated using the formula:
[tex]C=\pi d[/tex]Given that d = 1220 millimeters.
When π = 3.14
[tex]C=3.14(1220)=3830.8\; mm[/tex]When π = 3.14159
[tex]C=3.14159(1220)=3832.7398\; mm[/tex]Therefore, for Frank to improve the accuracy of measurement of the circumference, he can use 3.14159 for π.
Option D is correct.
10 - Mr. Sandler's CarAdam Sandler's car tire has a slow puncture which is losing pressure according to this formula: Pt=3000.94t where t is the time in minutes and Pt represents the tire pressure in kPa (kilopascals).If the recommended lowest tire pressure to drive safely is 73 kPa how much time does Adam Sandler have left before it is unsafe? Show your work.
The function P is given by:
[tex]P(t)=300(0.94)^t[/tex]The required time t is given by:
[tex]300(0.94)^t=73[/tex]Divide both sides of the equation by 300:
[tex]\begin{gathered} 0.94^t=\frac{73}{300} \\ t\ln(0.94)=\ln(\frac{73}{300}) \\ t=\frac{\ln(\frac{73}{300})}{\ln(0.94)}\approx22.84\text{ min} \end{gathered}[/tex]Therefore, the required time is approximately 22.84 min
All faces of a bench except the two faces that rest on the ground will be coated with a water resistant paint. The bench is a right prism. What is the total area to be coated with paint? Show your work.
Given:
All faces of a bench except the two faces that rest on the ground will be coated with a water-resistant paint.
So, the number of the sides that will be coated = 8 sides
The upper side with dimensions of 63 in and 16 in
Area = 63 * 16 = 1008 in²
Two sides of dimensions of 18.5 in and 16 in
Area = 2 * 18.5 * 16 = 592 in²
Two sides of dimensions of 14 in and 16 in
Area = 2 * 14 * 16 = 448 in²
Two sides on the front and behind, the one side will the difference of total rectangle and the space:
[tex]2(63*18.5-54*14)=819\text{ }in^2[/tex]One side that will face the ground of dimensions 54 in and 16 in
Area = 54 * 16 = 864 in²
So, the total area = 1008 + 592 + 448 + 819 + 864 = 3731 in²
so, the answer will be: Area = 3731 in²
Find the distance between point K and point L.Distance:Х2Continue© 2020 Meme Education. All Rights ReservedType here to searchоW!
We have to find the distance between point I=(-4, 7) and J=(4, 7).
If we use the expression for the distance for points in te xy-plane, we
Brock's dad is 24 years older than him.In 14 years, his dad will be twice his age at that time. How old is Brock right now?
Determine all solutions to the equation 1 over sine theta equals 2 times sine theta on the interval [0, 2π).If none of the options are correct, which would be the best choice?
The given trigonometry equation is,
[tex]\frac{1}{\sin\theta}=2\cos \theta[/tex]We are to get the solution under the interval 0 to 2pi. I will be resolving it graphically.
The graph is shown below
The solution to the equations on the graph is always where the two equations intersect each other on the graph.
Hence, from the graph we can obseved that they intersect each other at two points under the interval 0 to 2pi.
The two points are,
[tex](\frac{\pi}{4},\frac{5\pi}{4})[/tex]Therefore, the solution is
[tex](\frac{\pi}{4},\frac{5\pi}{4})[/tex]