Given the following equation,
[tex]\text{ 2\lparen2y - 16\rparen = 0}[/tex]Let's determine the value of y.
[tex]\text{ 2\lparen2y - 16\rparen = 0}[/tex][tex]\text{ }\frac{2(2y\text{ - 16\rparen}}{2}\text{ = 2}[/tex][tex]\text{ 2y - 16 = 0}[/tex][tex]\text{ 2y = 16}[/tex][tex]\text{ }\frac{2y}{2}\text{ = }\frac{16}{2}[/tex][tex]\text{ y = 8}[/tex]Therefore, y = 8
The answer is 8.
Solve for x. Round your awnser to the nearest tenth.
We are given a right triangle and we have to find the length of one of its sides. It will be useful to remember the definition of the tangent of an angle inside a right triangle. For an angle α<90° in a right triangle we have:
[tex]\tan \alpha=\frac{\text{opposite side}}{\text{adjacent side}}[/tex]If α is the 26° angle in the image then its opposite side is 11 and its adjacent side is x. Then we get:
[tex]\tan 26^{\circ}=\frac{11}{x}[/tex]We can multiply both sides of this equation by x:
[tex]\begin{gathered} \tan 26^{\circ}\cdot x=\frac{11}{x}\cdot x \\ \tan 26^{\circ}\cdot x=11 \end{gathered}[/tex]And we divide both sides by tan(26°):
[tex]\begin{gathered} \frac{\tan 26^{\circ}\cdot x}{\tan 26^{\circ}}=\frac{11}{\tan 26^{\circ}} \\ x=\frac{11}{\tan26^{\circ}}=22.6 \end{gathered}[/tex]Then the answer is 22.6.
Given the equation of the straight line AB is 3x+KY=8 where k is a constant. the straight line AB is parallel to the straight line connecting the point P(-1, 6) with the point Q(5, -3). Find the value of k then calculate the x-intercept of the straight line AB
If we have two parallel lines, than their slopes must be the same.
One way of comparing slopes of linear equations is to write them in the slope-intercept form:
[tex]y=mx+b[/tex]In this form, m is the slope and b is the y-intercept.
So, let's write the first equation in this form:
[tex]\begin{gathered} 3x+ky=8 \\ ky=-3x+8 \\ y=-\frac{3}{k}x+\frac{8}{k} \end{gathered}[/tex]To find the value of k, we can find the slope of the parallel line and compair it to the slope in this equation.
The slope of a line given two points on it can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]Since we have points (-1, 6) and (5, -3), we can calculate the slope of the parallel line:
[tex]m=\frac{-3-6}{5-(-1)}=\frac{-9}{5+1}=-\frac{9}{6}=-\frac{3}{2}[/tex]Since both lines are parallel, their slopes are the same.
We know that the slope of the first line is -3/k and the second line is -3/2, so, since they are parallel:
[tex]\begin{gathered} -\frac{3}{k}=-\frac{3}{2} \\ -3\cdot2=-3\cdot k \\ 2=k \\ k=2 \end{gathered}[/tex]Since we have the value for k, we can substitute it into the equation for AB:
[tex]\begin{gathered} y=-\frac{3}{k}x+\frac{8}{k} \\ y=-\frac{3}{2}x+\frac{8}{2} \\ y=-\frac{3}{2}x+4 \end{gathered}[/tex]To find the x-intercept, we can see that it happens when the value of y is equal to 0, so we can plug in y = 0 and find the value of x:
[tex]\begin{gathered} y=0 \\ 0=-\frac{3}{2}x+4 \\ \frac{3}{2}x=4 \\ x=\frac{2}{3}\cdot4 \\ x=\frac{8}{3} \end{gathered}[/tex]So, the value of k is 2 and the x-intercept is 8/3.
You invest $3,150.00 in a stock plan. The first year, it loses 5% of its value. The second year, it gains 9% of its value. What is the difference between the value of your stocks at the end of the second year and your initial investment?
Given:
The investment is $3,150.00.
The loss percent for the first year is 5 %.
The gain percent for the second year is 9 %.
Required:
We need to find the investment amount at end of the second year.
Explanation:
The investment amount at the end of the first year is
[tex]=3150(1-\frac{5}{100})[/tex][tex]=3150(1-0.05)[/tex][tex]=2992.5[/tex]The investment amount at the end of the first year is $2992.5.
The investment amount at the end of the second year is
[tex]=2992.5(1+\frac{9}{100})[/tex][tex]=2992.5(1+0.09)[/tex][tex]=3261.825[/tex][tex]=3261.83[/tex]The investment amount at the end of the second year is $3261.83.
Final answer:
The investment amount at the end of the second year is $3261.83.
18, 32Using rounding, what is the best estimate for the product of these numbers?200300600800
We are given the following two numbers
18 and 32
Using rounding, what is the best estimate for the product of these numbers?
We can round up 18 to 20
We can round down 32 to 30
20×30 = 600
Therefore, the best estimate for the product of 18 and 32 is 600.
27. The following chart represent the cost, Cd), in dollars, of a pizza in relation to its diameter, d, in inches. What is the average rate of change in cost from an 8 in to a 16 in pizza. d Cd) 8 2.51 103.93 125.65 147.70 16 10.05
The average rate of change is the ratio of the absolute change in one quantity divided by the absolute change in another quantity. Usually, the first one is dependent on the second one.
An 8 in pizza costs $2.51.
A 16 in pizza costs $10.05.
The absolute change in the cost is:
[tex]10.05-2.51=7.54[/tex]The absolute change in the diameter is:
[tex]16-8=8[/tex]Then, the average rate of change of the cost with respect to the diameter is:
[tex]\frac{7.54}{8}=0.9425[/tex]Therefore, to the nearest hundredth, the average rate of change in the cost from an 8in to a 16 in pizza, is:
[tex]0.94[/tex]Solve the following logarithmic equation. Express all solutions in exact form.√log x-3 =log x-3
Square both side of equation and simplify the equation.
[tex]\begin{gathered} (\sqrt[]{\log x-3})^2=(\log x-3)^2 \\ \log x-3=(\log x)^2-6\log x+9 \\ (\log x)^2-6\log x-\log x+9+3=0 \\ (\log x)^2-7\log x+12=0 \end{gathered}[/tex]Assume log x = y. So equation is,
[tex]y^2-7y+12=0[/tex]Simplify the equation to obtain the value of y.
[tex]\begin{gathered} y^2-7y+12=0 \\ y^2-4y-3y+12=0 \\ y(y-4)-3(y-4)=0 \\ (y-3)(y-4)=0 \\ y=3,4 \end{gathered}[/tex]So the value of y is 3 or 4,
[tex]\begin{gathered} \log x=3 \\ x=e^3 \end{gathered}[/tex]Or
[tex]\begin{gathered} \log x=4 \\ x=e^4 \end{gathered}[/tex](x squared -9x -7) -(7x squared +2x +3) Find the difference
ANSWER
[tex]-6x^2-11x-10[/tex]EXPLANATION
We want to find the difference between the two expressions:
[tex](x^2-9x-7)-(7x^2+2x+3)[/tex]To do this, we will subtract like terms from one another.
That is:
[tex]x^2-7x^2-9x-2x-7-3[/tex]Simplifying the expression, we have:
[tex]-6x^2-11x-10[/tex]That is the answer.
find the missing angletan x= 0.9004
We are told that the tangent of an angle x is equal to 0.9004. In order to solve this equation for x we can use the arctangent function that has this property:
[tex]\tan^{-1}(\tan x)=x[/tex]Then we can apply the arctangent to both sides of our equation:
[tex]\begin{gathered} \tan^{-1}(\tan x)=\tan^{-1}0.9004 \\ x=\tan^{-1}0.9004 \end{gathered}[/tex]So our angle is the arctangent of 0.9004 which can be found using a calculator. However calculators oftenly work with radians and we need to express x in degrees. In order to transform the result from radians to degrees we have to perform the following operation:
[tex]x=\tan^{-1}0.9004\cdot\frac{360}{2\pi}=41.999872^{\circ}[/tex]AnswerWheter we round to the nearesth tenth, hundreth or thousanth the answer is 42°.
Find AB if BC is 20 and AD is 24
BC = 20
If < B = 67
Then
Th using the sine rule
[tex]\frac{\sin\text{ 67}}{AB}=\frac{\sin 46}{20}[/tex]cross -multiply
[tex]AB\text{ sin 46=20sin67}[/tex]Divide both-side of the equation by sin46
[tex]AB\text{ =}\frac{20\sin 67}{\sin 46}[/tex][tex]AB\approx25.59[/tex]The area of the entire figure below is 111 square unit.The area of the entire figure below is 111 square unit.
Looking at the image, the width of the rectangle is 7 small rectangles and the length is 9 small rectangles, therefore the area of 1 square unit is equal to 9 * 7 = 63 small rectangles.
From these small rectangles, an area of 5 * 4 = 20 small rectangles is shaded.
Therefore the shaded area is calculated as:
[tex]\frac{20}{63}\cdot1\text{ square unit}=\frac{20}{63}\text{ of a square unit}[/tex]Charlie is saving money to buy a game. So far he has saved $20, which is one-fourth of the total cost of the game. how much does the game cost?
Let 'x' represent the cost of the game.
Therefore, one-fourth of the total cost of the game is
[tex]\begin{gathered} \frac{1}{4}\text{ of x=20} \\ \frac{1}{4}x=20 \end{gathered}[/tex]Evaluate for x
[tex]x=20\times4=80[/tex]Hence, the total cost of the game is $80.
1 point The following expression represents monthly growth. What is the yearly rate of growth? (1.04)^m
(1.04)^m
m= Months
One year has 12 months_
(1.04)^12 = 1.60
0.60 = yearly rate of growth
Simplify the following: -(3z)²
We have the following general rule for exponents:
[tex](a\cdot b)^n=a^n\cdot b^n[/tex]Then, in this case we have:
[tex]-(3z)^2=-(3^2\cdot z^2)=-9z^2[/tex]therefore, the simplifed expression is -9z²
For a standard normal distribution, find:P(Z > -1.79)Express the probability as a decimal rounded to 4 decimalplaces.
Given the probability:
[tex]P(Z>-1.79)[/tex]To find this probability, you have to use the tables for the standard normal distribution. These tables show the accumulated probability for the Z-distribution, this means that you can find the probability up to a determined Z-value. To find the probability above a determined Z-value you have to use the complementary probability, that is:
[tex]P(Z>-1.79)=1-P(Z\leq-1.79)[/tex]- First, use the Z-table to find the accumulated probability until Z=-1.79, the Z-value is negative, so you have to use the left entry of the table:
In the first column, you will find the first two digits of the Z-value, and in the first two, you will find the third digit of the Z-value, and in the body of the table, all accumulated probabilities are listed.
Cross the corresponding row and column to find the accumulated probability:
Then the accumulated probability until -1.79 is:
[tex]P(Z\leq-1.79)=0.0367[/tex]Now that you found the accumulated probability, you can use the complement to find the probability above -1.79
[tex]\begin{gathered} P(Z>-1.79)=1-P(Z\leq-1.79) \\ P(Z>-1.79)=1-0.0367 \\ P(Z>-1.79)=0.9633 \end{gathered}[/tex]Write the function in slope intercept form Maya wants to rent a bike at the beach The cost includes a rental fee and a price per half hour
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
We can find the slope and y-intercept of our line by using two points from the graph and solving the system. I'm going to use (0, 10) and (2.5, 20), but you can use any pair of points that belong to the line.
From the first point we already have our y-intercept, if we substitute this point at the slope-intercept form we have
[tex]10=m\cdot0+b\Rightarrow b=10[/tex]Using this value for b in our form and using the second point, we can find our slope
[tex]\begin{gathered} 20=2.5m+10 \\ 10=2.5m \\ \frac{10}{2.5}=m \\ m=4 \end{gathered}[/tex]This means that our line equation is
[tex]y=4x+10[/tex]how many marriage licenses were issued in 2006 ? round answer to the nearest hundred
To solve the exercise we have to replace the value requested on the equation given to model the problem as above
[tex]y=3.4905(2006)^2-17674(2006)+21533000=124853.658[/tex]As we see and approximating the result to the options, we get that the correct answer is the second one (124900)
what theorems or postulates could you use to prove this relationship
From the diagram given, we can see that line a is parallel to line b. This means that the position of each of the angle on line a is equal to the position of each of the angle in line b
From the figure <1 = <(7x+19)degree (corresponding angle). Also <5 = 7x+19 = <1 (corresponding angle as well)
From the above, we can say that <5 = <1 and since <5 and <6 lies on the same stright line, their sum will be 180.
Don't forget that <5 is now replaced as <1. Hence <1+<6 = 180 (supplementary angle).
From the expalnation above, the theorems that was used to prove the relationship between <1 and <6 are supplementary angle, corresponding angle and same side interior angle
Hence option D is correcct
Hello I need help with this problem for my home work here’s a picture
The Solution:
Given:
We are required to find the equivalent of the given expression.
Simplifying the given expression, we get:
[tex]4x^2\sqrt{5x^4}\cdot3\sqrt{5x^8}=4x^2\times x^2\sqrt{5}\times3x^4\sqrt{5}[/tex][tex]=4x^2\times x^2\times3x^4\times\sqrt{5}\times\sqrt{5}=4x^4\times3x^4\times5=60x^8[/tex]Therefore, the correct answer is [option B]
At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the number of loans X that a
randomly selected loan agent closes on a randomly selected day has the probability distribution below.
4
5 6
P(x) 0.05 0.10 0.22 0.30 0.18 0.12 0.03
X
1
2
3
At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan
agent on a randomly selected day.
Which is the mean of X?
Which is the mean of Y?
V
Which is the standard deviation of X?
7
which is the standard deviation of Y
The mean of X is E(X)=$3.94
The mean of Y is E(Y)=$347
The standard deviation of X is $1.4129
The standard deviation of Y is $220.645
What is meant by mean and standard deviation?The mean is the set of two or more numbers' mathematical average. It is possible to calculate two different types of means: the arithmetic mean and the geometric mean. Add the numbers in a set together and divide by the total number of numbers in the set to find the arithmetic mean.
Standard deviation, which is the square root of the means of the squared deviations from the arithmetic mean, is also known as root-mean square deviation. To quantify the risks associated with an investment instrument, standard deviation is used in finance.
The computation is shown below:
Y = a +bX
where,
Y = money earned by a randomly chosen
a = $150
b = $50
X = number of loan
Now,
E(X) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)
=$3.94
E(X) =$3.94
Therefore, mean of X is $3.94
Now,
E(y) = $150 + ($50 × 3.94)
= $347
E(y) =$347
Therefore, mean of Y is $347
Variance=∑[tex]P_{i}[/tex]([tex]X_{i}[/tex]-μ)
=0.43218+0.37636+0.194392+0.00108+0.202248+0.509232+0.280908
=1.9964
Standard deviation=√variance
=√1.9964
=1.4129
Therefore, the standard deviation of X is $1.4129
Y=a+bX
Y=$150+($50×1.4129)
Y=$220.645
Therefore, the standard deviation of X is $220.645
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Travis scored 18 points in the first basketball game of the season. He scored 3 fewer point in the second game than in the first game. find the total number of point Travis scored in the first and second games.
Let's call the number of points scored in the first game A and the number of points scored in the second game B:
A = 18
since he scored 18 points in the first
B = A -3 = 18 - 3 = 15
B = 15
since he scored 3 fewer point in the second
The total number of point is
A + B = 18 + 15 = 33
Triangle ABC has vertices A(1,3), B(2,5), and C(5,3). What are the coordinates of B after the translation described by the rule T(1,4)?B =
Answer:
B' (3, 9)
Explanation:
Given the coordinates of vertices of a triangle A(1,3), B(2,5), and C(5,3), if the triangle is translated by T(1, 4), the coordinates of the new triangle will be expressed as:
A' = (1, 4) + A(1, 3)
A' = (1+1, 4+3)
A' = (2, 7)
B' = (1, 4) + B(2, 5)
B' = (1+2, 4+5)
B' = (3, 9)
C' = (1, 4) + C(5, 3)
C' = (1+5, 4+3)
C' = (6, 7)
From the calculation above, it can be seen that the coordinates of B after translation is B' (3, 9)
Felicia is considering two companies for the installation of her new carpet. The carpet companies installation rates are shown.Carpet Company A: C = 1.35y + 100 where c is the cost and y is the number of square yards.Carpet Company B: This company charges $2.05 per square yard for the carpet and the installation.Identity the unit rate in dollars per square yard for each carpet company.Part 2 is asking me "Which company has the greatest rate of change? Explain how this would affect the slope when graphed on a coordinate plane"
The cost for a unit square yard is given as:
Company A = $101.35 per square yard
Company B charges $2.05 per square yard
Company B has the greatest slope. The line for Company B is steeper as a result of this.
Explanation:Company A:
C = 1.35y + 100
The cost for a unit square yard is given as:
C = 1.35(1) + 100
= $101.35
Company B charges $2.05
Part 2
Company B has the greatest slope. The line for Company B is steeper as a result of this.
Enter an equation in standard form to model the linear situation.A bathtub that holds 52 gallons of water contains 17 gallons of water. You begin filling it, and after 5minutes, the tub is full
First step is to find the slope of the linear situation
Use (0,17) and (5,52) as the given points
[tex]m=\frac{52-17}{5-0}=\frac{35}{5}=7[/tex]y intercept is 17, then the linear equation in slope intercept form is
[tex]y=7x+17[/tex]Now, clear 17 from this equation to find the standard form
[tex]\begin{gathered} y=7x+17 \\ -7x+y=17 \end{gathered}[/tex]A school wants to put a bond in the next election, they call this bond Measure K. Before puttingthe bond on the ballot, they want to see how much support they would have from voters in thecounty. They select a random sample of voters in the county, and find a 90% confidence intervalfor the proportion of voters in this county who would vote yes. In order to do this, they neededto use:(Multiple choice)O 1 proportion (z) confidence intervalO 1 proportion (2) hypothesis testO 2 proportion (z) confidence intervalO 2 proportion (2) hypothesis test
A school wants to put a bond in the next election, they call this bond Measure K.
They select a random sample of voters in the county and find a 90% confidence interval for the proportion of voters in this county who would vote yes.
Recall that a hypothesis test is used when we want to test an assertion or a claim.
For the given case, there is no assertion or any claim so this is definitely not a hypothesis test.
This is in fact a confidence interval since we are interested in the proportion of voters in this county who would vote yes.
The confidence interval would give us a fair estimate of the true population proportion of voters in this county who would vote yes.
Now coming to whether is it a 1 proportion or 2 proportion confidence interval.
Notice that there is only 1 proportion for the given case that is the proportion of voters in this county who would vote yes.
Therefore, the need to use "1 proportion (z) confidence interval"
Triangles RTS and XYZ are similar. Match each given side of triangle XYZ with the corresponding side on triangle RTS. R À À S TY YZ XY 111 XZ :: RS :: RT :: TS hp
we know that
if the triangles are similar, thrn itcs corresponding sides are proportional
so
In this problem
the corresponding sides are
YZ and TS
XY and RT
XZ and RS
simplify 7.5y⁴ • 9y²
Answer:
67.5y⁶.
Explanation:
Given the expression:
[tex]7.5y^4\times9y^2[/tex]First, reorder the terms:
[tex]=7.5\times9\times y^4\times y^2[/tex]Next, combine like terms:
[tex]\begin{gathered} =67.5\times y^4\times y^2 \\ =67.5\times y^{4+2} \\ =67.5\times y^6 \\ =67.5y^6 \end{gathered}[/tex]The simplified form is 67.5y⁶.
Which equation could be used to find how many soft drink refills Ryan ordered
Solution
We are given
Restaurant charge = $16.99
Soft drink refill charge each = $1.75
Ryan paid = C
Let x denotes the number of soft drink refill Ryan ordered, so we have
[tex]16.99+1.75x=C[/tex]Therefore, the answer is
[tex]1.75x+16.99=C[/tex]A recipe uses 111cups of milk to make 10 servings. If the same amount of milk is used foreach serving, how many servings can be made using 1 gallon of milk?Show your work.ka1 pint = 2 cups1 quart = 2 pints1 gallon = 4 quartsHelp!
1 gallon --------------------- 4 quarts
1 quarts ------------------- 2 pints
4 quarts --------------- x
x = 8 pints
1 pints ------------------------ 2 cups
8 pints ---------------------- x
x = 16 cups
1.25 cups ----------------------- 10 servings
16 cups ------------------------ x
x = 12.8 servings
It is possible to made 12.8 servings
In a survey of 100 people, 7 out of every 25 said that Abraham Lincoln was the greatest U.S President. What percent of people surveyed does this represent?
28%
EXPLANATION
Percentage of people surveyed that said Abraham Lincoln was the greatest U.S president is;
[tex]=\frac{7}{25}\times100[/tex][tex]=\text{ 28 \%}[/tex]Jacob drove 78 miles in 2 2/3 hours. If he drove at a constant rate, how far did he travelin one hour? Enter your answer as a whole number, proper fraction, or mixednumber in simplest form.
In order to calculate the distance travelled in one hour, we can divide the total number of miles by the amount of time required for that number of miles:
[tex]\text{speed}=\frac{78}{2\frac{2}{3}}=\frac{78}{(2+\frac{2}{3})}=\frac{78}{\frac{6}{3}+\frac{2}{3}}=\frac{78}{\frac{8}{3}}=78\cdot\frac{3}{8}=\frac{39\cdot3}{4}=\frac{117}{4}[/tex]So in one hour, the distance travelled is 117/4 miles.
Converting this value into a mixed number, we have:
[tex]\frac{117}{4}=\frac{116}{4}+\frac{1}{4}=29+\frac{1}{4}=29\frac{1}{4}[/tex]--------
Done!
Do you have any questions about the answer?