(h,k) are the coordinates of the vertex.
Use the given point (x,y) and the vertex (h,k) in the equation above to find the value of a:
Point: (-3 ,1) x = -3 y=1
Vertex: (-4 , -2) h= -4 k=-2
[tex]\begin{gathered} 1=a(-3-(-4))^2+(-2) \\ 1=a(-3+4)^2-2 \\ 1=a(1)^2_{}-2 \\ 1=a-2 \\ 1+2=a \\ 3=a \end{gathered}[/tex]Use the vertex and a to write the equation:
[tex]\begin{gathered} y=3(x-(-4))^2+(-2) \\ \\ \\ y=3(x+4)^2-2 \end{gathered}[/tex]309+23143240-59234881
Given data:
The given numbers are 309+23143240-59234881.
The simplification of the given numbers is,
-36091332.
Instructions: Find the circumference of the circle and round to the nearest tenth.
The circumference of the circle formula is
[tex]C=2\pi r[/tex][tex]r\rightarrow radius[/tex][tex]\begin{gathered} diameter=7.8yd \\ r=\frac{diameter}{2}=\frac{7.8}{2}=3.9yd \\ \end{gathered}[/tex][tex]\begin{gathered} C=2\pi r \\ C=2\times\pi\times3.9 \\ C=24.5yd \end{gathered}[/tex]Hence, the circumference of the circle is 24,5yd
The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual who is a female or prefers science?
Gender Favorite Subject Total
Math English Science
Male 0.200 0.050 0.175 0.425
Female 0.100 0.325 0.150 0.575
Total 0.300 0.375 0.325 1.000
Answer: 2
Step-by-step explanation: 0.300 0.375 0.325 1.000 = 2
does (51, 58) make the equation y =x -7 true?
The objective is to verify whether the point (51,58) maes the equation y=x-7.
Substitute the values of x and y coordinate in the given equation.
[tex]\begin{gathered} y=x-7 \\ y-x=-7 \\ 58-51=-7 \\ 7=-7 \end{gathered}[/tex]Since, LHS is not equal to RHS.
Thus, the coordinate (51,58) does not make the equation y=x-7.
Hence the answer is NO.
what is 0.554 / 0.041
Answer:
13.5
Step-by-step explanation:
Hello!
Here is your solution after dividing the given decimals.
[tex]0.554[/tex] ÷ [tex]0.041[/tex] = [tex]13.51219[/tex] ← (There is a line passing over all numbers to the right side of the decimal.)
In summary, the final answer is 13.5 ← (Line over 5)
Hope this helps!
My answer is correct or no please check
Answer:
D) 5 minus a number M
hope this helps!
Answer:
Yep. You got it right. Good job!
Step-by-step explanation:
Amy’s grandmother is exactly 6 times older than Amy.
Which three statements below must be true?
The three statements that are true include:
Amy's age is a factor of the age of her grandmother.
The age of Amy's grandmother is a composite number.
The number 6 is a factor if the age of Amy's grandmother.
What is a factor?A factor simply means a number that can be multiplied by another number to get the original number.
Let's say Amy is 10 years. The grandmother will be 69 years. In this case, 10 is a factor of 60. Therefore, Amy's age is a factor of the age of her grandmother.
The complete options are given below.
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Which three statements below must be true?
1.The age of Amy’s grandmother is a prime number.
2.Amy’s age is a factor of the age of her grandmother.
3.The age of Amy’s grandmother has exactly two factors.
4.The age of Amy’s grandmother is a composite number.
5.The number 6 is a factor of the age of Amy’s grandmother.
6.The age of Amy’s grandmother has exactly four factors.
solve each system by substitution.y =-2x + 5y =-8x+17
To solve the equation system by substitution, since the equations are expressed in terms of y, you have to equal both expressions and calculate the value of x:
[tex]\begin{cases}y=-2x+5 \\ y=-8x+17\end{cases}[/tex][tex]\begin{gathered} y=y \\ -2x+5=-8x+17 \end{gathered}[/tex]To calculate the value of x, the first step is to pass the x-term to the left side of the equation by applying the opposite operation:
[tex]\begin{gathered} -2x+8x+5=-8x+8x+17 \\ 6x+5=17 \end{gathered}[/tex]Next, pass 5 to the right side of the equation:
[tex]\begin{gathered} 6x+5-5=17-5 \\ 6x=12 \end{gathered}[/tex]Finally, divide both sides by 6 to reach the value of x
[tex]\begin{gathered} \frac{6x}{6}=\frac{12}{6} \\ x=2 \end{gathered}[/tex]Now that we have determined the value of x, replace it in either one of the original equations to determine the value of y:
[tex]\begin{gathered} y=-2x+5 \\ y=-2\cdot2+5 \\ y=-4+5 \\ y=1 \end{gathered}[/tex]The solution for this equation system is (2,1)
The cargo of the truck welghs no more than 2,800 pounds.Use w to represent the weight (in pounds) of the cargo.
We know that
• The truck weighs no more than 2,800 pounds.
This problem is about inequalities.
"no more" indicates an inequality sign, specifically, it shows that we should use "less than or equal to", because this sign indicates the same as the problem do.
Therefore, the expression of the truck weight is
[tex]w\leq2,800[/tex]The administrator at your local hospital states that on weekends the average wait time for emergency room visits is 11 minutes. Based on discussions you have had with friends who have complained about how long they wait to be seen in the ER over a weekend, you dispute the administrator's claim. You decide to test your hypothesis. Over the course of a few weekends, you record the wait time for 28 randomly selected patients. The average wait time for these selected patients is 12 minutes with a standard deviation of 2.5 minutes. Do you have enough evidence to support your hypothesis that the average ER wait time is longer than 11 minutes? Conduct your test with a 5% level of significance.
This is a hypothesis test for the population mean.
The claim is that on weekends the average wait time for emergency room visits is more than 11 minutes.
Then, the null and alternative hypothesis are:
[tex]\begin{gathered} H_0\colon\mu=11 \\ H_a\colon\mu>11 \end{gathered}[/tex]The significance level is 0.05.
The sample has a size n=28.
The sample mean is M=12.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.5.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2.5}{\sqrt{28}}=0.4725[/tex]Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{12-11}{0.4725}=\dfrac{1}{0.4725}=2.117[/tex]The degrees of freedom for this sample size are:
[tex]df=n-1=28-1=27[/tex]This test is a right-tailed test, with 27 degrees of freedom and t=2.117, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>2.117)=0.0218[/tex]As the P-value (0.0218) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
Conclusion: at a significance level of 0.05, there is enough evidence to support the claim that, on weekends, the average wait time for emergency room visits is more than 11 minutes.
WhaGraph the piecewise-defined function. Use the graph to determine the domain and range of the function. x + 2 if x < -1F(x)={ - 2x + 3 if x ≥ - 1
The domain of the function is all possible x-values a function can have; therefore, we see here that the domain of the function is all real numbers (including -1).
The range of a function is all possible y values a function can take. We see from the graph above that can take only the values that are greater than or equal to 1; therefore, the range of the function is all real numbers greater than or equal to 1.
A translation 6 units right maps P onto P'. Complete the translation function.
If we have a point P=(x,y) and we apply a translation 6 units to the right we will get a point P' that is:
[tex](x,y)\longrightarrow(x+6,y)[/tex]We can test it by trying with P=(0,0).
Then P' would be (6,0), that is 6 units to the right from P.
Answer: (x,y) --> (x+6,y)
I don’t understand how to get the second x intercept
In this problem
the vertex is given ------> (40/2,12)-------> (20,12)
The first intercept is (0,0)
therefore
second intercept is
x-intercept=20+20=40
(40,0) is the coordinates of the second x-intercept
(the vertex is the midpoint between the first and second x-intercept)
see the attached figure
This is not from a test or graded assessment. The Question is included in the picture.
Given:
[tex]\begin{gathered} g(x)=-x^5-4x^3+6x \\ \\ h(x)=x^4+2x^3-2x^2+x-7 \\ \\ j(x)=3x^4+7x^2 \end{gathered}[/tex]It's required to determine if the functions are odd, even, or neither.
An even function satisfies the property:
f(-x) = f(x).
And an odd function satisfies the property:
f(-x) = -f(x)
We substitute x by -x on each function as follows:
[tex]\begin{gathered} g(-x)=-(-x)^5-4(-x)^3+6(-x) \\ \\ g(-x)=x^5+4x-6x \end{gathered}[/tex]Note the function g(-x) is the inverse (negative) of g(x), thus,
g(x) is odd
Now test h(x):
[tex]\begin{gathered} h(-x)=(-x)^4+2(-x)^3-2(-x)^2+(-x)-7 \\ \\ h(-x)=x^4-2x^3-2x^2-x-7 \end{gathered}[/tex]Comparing h(-x) and h(x) we can see none of the properties are satisfied, thus:
h(x) is neither odd nor even
Let's now test j(x):
[tex]\begin{gathered} j(-x)=3(-x)^4+7(-x)^2 \\ \\ j(-x)=3x^4+7x^2 \end{gathered}[/tex]Since j(-x) and j(x) are equal,
j(x) is even
find the surface area of the cone in terms of pi. SA=__ cm squared. simply
Given the figure of a cone.
As shown, the slant height = s = 23 cm
And the diameter of the base = d = 18 cm
So, the radius = r = 0.5d = 9 cm
The surface area of the cone will be calculated using the following formula:
[tex]SA=\pi rs+\pi r^2[/tex]Substitute s = 23, and r = 9, writing the surface area in terms of π
[tex]SA=π(18)(23)+π(9)^2=414π+81π=495π[/tex]So, the answer will be:
The surface area of the cone = 495π cm²
It takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make twoomelets. What is the cost per omelet if eggs cost $.99 per dozen,1 lb of cheese costs $4.29, and 1/2 lb of butter costs $1.25?a. $2.15b. $1.34c. $1.08d. $.31
Given:
It takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make two
omelets
Eggs cost per dozen = $0.99
So, the cost of 6 eggs = 0.99/2 = 0.495
1 lb of cheese costs $4.29
1 lb = 16 oz
So, the cost of 5 oz =
[tex]\frac{5}{16}\cdot4.29=1.34[/tex]1/2 lb of butter costs $1.25
So, the cost of 2 oz =
[tex]\frac{2}{8}\cdot1.25=0.3125[/tex]So, the cost of two omelets = 0.495+1.34+0.3125 = 2.1475
So, the cost of one omelet = 2.1475/2 ≈ 1.08
So, the answer will be option c. $1.08
WILL GIVE BRAINLYEST 200 PO9NTS SENCE IM GIVING EXTRA
The range of the data set increased by 12 and the median of the data set is at 50.
Range of a Data SetThe Range of a data set is the difference between the lowest and highest values.
The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest. The answer gives you the range of the list.
The given data set is;
15, 17, 19, 19, 22, 23, 25, 27, 32, 34
The range of this data set will be
range = 34 - 15 = 19.
Assuming we add another age of 46, the range will become
range = 46 - 15 = 31
This will impact the range of the data by 31 - 19 = 12.
The range will be impacted by an increase with 12.
Median of a Data SetThe median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points.
The data set given is
48, 63, 75, 40, 32, 52, 35, 68, 83, 40
We have to rearrange the data points first before finding the median;
32, 35, 40, 40, 48, 52, 63, 68, 75, 83.
The median of the data set will be the average between 48 and 52 which is 50.
the median of the data is 50.
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Tents-R-Us makes and sells tents. Tents-R-Us' motto is“Keep It Simple.” The company decides to makes justthree sizes of tents: the Mini, the Twin, and theFamily-Size. All the tents they make have equilateraltriangular ends as shown at right.1. For the Twin, each edge of the triangle will be 8 ft. Find the heightof the tent at the center, correct to the nearest inch. One way to findthis height is to make an accurate scale drawing and measure.
The company decides to make just three sizes of tents: the Mini, the Twin, and the Family-Size.
The shape of these tents is an equilateral triangle.
Part 1:
For the Twin, each edge of the triangle will be 8 ft.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 8 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=8\cdot\frac{\sqrt[]{3}}{2} \\ h=4\sqrt[]{3} \\ h=6.9\: ft \end{gathered}[/tex]Therefore, the height of the Twin tent at the center is 6.9 ft
Part 2:
The Mini tent will have edges 5 ft long.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 5 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=5\cdot\frac{\sqrt[]{3}}{2} \\ h=4.3\: ft \end{gathered}[/tex]Therefore, the height of the Mini tent at the center is 4.3 ft
Part 3:
The Family-Size tent will have a height of 10 ft at the center.
Recall that the height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Re-writing the formula for edge (a)
[tex]a=h\cdot\frac{2}{\sqrt[]{3}}[/tex]Since we are given that h = 10 ft
[tex]\begin{gathered} a=h\cdot\frac{2}{\sqrt[]{3}} \\ a=10\cdot\frac{2}{\sqrt[]{3}} \\ a=\frac{20}{\sqrt[]{3}} \\ a=11.6\: ft \end{gathered}[/tex]Therefore, the length of edges of the Family-Size tent is 11.6 ft
Evaluate the rational expression for the given x value. Express the answer as a fraction in simplest form.
Given the expression:
[tex]\frac{x-3}{2x+3}[/tex]We need to find the value of the expression when x = 7
So, we will substitute with x = 7 into the expression as follows:
[tex]\frac{7-3}{2\cdot7+3}=\frac{7-3}{14+3}=\frac{4}{17}[/tex]so, the answer will be 4/17
Mark went to the bank to borrow $10,000. He was given 2 options for a $10,000 loan:OPTION 1: 24-month payback at 6%interest will result in a monthly payment of $443.21 per month, or OPTION 2: 36-month payback at 6% interest will result in a monthly payment .of $304.22 per month.Which statement is NOT true?F. Mark will pay a total of $10,637.04 if he chooses Option 1.G. Mark will pay a total of $10,951.92 if hechooses Option 2.H. Mark will save $314.88 if he selects Option 2.J. Mark will pay a lower total amount if he selects Option 1.
Loan= $10.000
Bank options:
24-month payback 6% interest, with a monthly payment of $443.21/month
Then, Mark in option 1 will pay a total of:
[tex]443.21\text{ x 24 months=}10,637.04\text{ in option 1. }[/tex]36-month payback 6% interest, with a monthly payment of $304.22/month.
Mark in option 2 will pay a total of:
[tex]304.22\text{ x 36months=}10,951.92\text{ in option 2. }[/tex]Then, Mark will pay a lower total amount of money if he selects option 1 (10.637.04 is less than 10,951.92), saving a total of:
[tex]10,951.92\text{ - 10.637.04= 314.88 if he chooses option 1. }[/tex]Therefore, the statement that is NOT true is:
H. Mark will save $314.88 if he selects option 2.
random variables, probability distributions and expected value Alyssa likes to play roulette, but she doesn't like the low probability of betting on a single number. Therefore, she bets on a block of 4 numbers, increasing her probability of winning to 38. She generally places a $5 chip on her block of 4. If any other number comes up she loses her bet, but if one of her 4 numbers come up, she wins $40 (and gets to keep her bet!). What is the expected value for Alyssa playing roulette? Round to the nearest cent. Do not round until your final calculation.
We have to calculate the expected value for Alyssa playing roulette.
The expected value is calculated as the weighted sum of all the possible the outcomes, weighted by the probabilities of occurrence of this outcomes.
Then, we start by listing all the outcomes:
1) One of the numbers of the block comes up.
This will happen with a probability of 4 out of 38 (P=4/38). NOTE: The total numbers of the roulette are 38.
The net prize, that is excluding the $5 she bets, is $40.
2) None of the numbers of the block comes up.
That will happen with probability 34 out of 38 (P=34/38).
The net prize, as she will lose the $5 she bets, is -$5.
The expected value can be calculated as:
[tex]E=\sum ^2_{i=1}p_i\cdot X_i=\frac{4}{38}\cdot40+\frac{34}{38}\cdot(-5)=\frac{160}{38}-\frac{170}{38}=\frac{-10}{38}\approx-0.26[/tex]The expected value for Alyssa is -$0.26.
2. Given: ZMOP is a right angle RP I OP Prove: MO || RP
Given that;
[tex]\begin{gathered} \measuredangle MOP\text{ is a right angle.} \\ \measuredangle MOP=90^0 \end{gathered}[/tex]And;
[tex]\vec{RP}\perp\vec{OP}[/tex]Since line RP is perpendicular to line OP, Angle RPO must be a right angle.
[tex]\measuredangle RPO=90^0[/tex]Recall that for two parallel lines intersected by a straight line, Same side interior angles are supplementary.
[tex]A+B=180^0[/tex]So, for line MO to be parallel to line RP, the sum of angle MOP and angle RPO must be equal to 180 degree.
[tex]\measuredangle MOP+\measuredangle RPO=90+90=180^0[/tex]Since the sum of angle MOP and angle RPO is equal to 180 degree, then line MO is parallel to line RP.
[tex]\begin{gathered} \text{ Since} \\ \measuredangle MOP+\measuredangle RPO=180^0 \\ \text{Then;} \\ MO\Vert RP \end{gathered}[/tex]Proved
Jacob took a taxi from his house to the airport. The taxi company charged a pick-upfee of $1.30 plus $5 per mile. The total fare was $16.30, not including the tip. Writeand solve an equation which can be used to determine , the number of miles in the
Let the total number of fare be f and total number of miles be m.
Therefore, the total fare f is given by:
[tex]f=1.30+5m[/tex]Substitute f = 16.30 into the equation:
[tex]\begin{gathered} 16.30=1.30+5m \\ 16.30-1.30=5m \\ 15=5m \\ \frac{15}{5}=\frac{5m}{5} \\ 3=m \\ m=3 \end{gathered}[/tex]Therefore, the required number of miles is 3.
Calculate the probability of winning: Roll two standard dice. You win if you get a sum of 4 or get a sum of 8. Round answer to one decimal place, for example if your answer is 0.65 enter 0.7
SOLUTION
The possible outcomes for sum of numbers when rolling two dice is shown
The total possible outcome is 36
The possible number of outcome of obtaining a 4 is 3
Therefore the probability of getting a sum of 4 is
[tex]\frac{3}{36}=\frac{1}{12}[/tex]The possible number of outcome of obtaining a 8 is 5
Therefore the probability of getting a sum of 8 is
[tex]\frac{5}{36}[/tex]Hence the probability of getting a sum 4 or a sum of 8 is
[tex]\frac{1}{12}+\frac{5}{36}[/tex]This gives
[tex]0.2[/tex]Therefore the probability of getting a sum 4 or a sum of 8 is 0.2
2 ABC Company has a large piece of equipmentthat cost $85,600 when it was first purchased 6years ago. The current value of the equipment is$30,400. What is the average depreciation of theequipment per year?F. $ 5,800G. $ 9,200H. $15,200J. $27,600K. $42,800
The intial cost of the equipment is C, which is given as 85,600.
The present value is PV, which is given as 30,400.
This simply means the total depreciation over the last 6 years can be derived as;
Depreciation = C - PV
Depreciation = 85600 - 30400
Depreciation = 55200
However, the method of depreciation is not given/specified, and hence the question requires that you calculate the average depreciation per year. That is, the total depreciation would be evenly spread over the 6 year period (which assumes that the depreciation per year is the same figure)
Average depreciation = Total depreciation/6
Average Depreciation = 55200/6
Average Depreciation = 9200
The correct option is option G: $ 9,200
Assume the normal distribution of data has a mean of 14 and a standard Deviation of 3. use the 65-95-99.7 rule to find the percentage of values that lie below 8
By the 65-95-99.7 rule,
[tex]\begin{gathered} 65\text{ \% of the distribution lies below }\bar{x}+\sigma\text{ and above }\bar{x}-\sigma \\ 95\text{ \% of the distribution lies below }\bar{x}+2\sigma\text{ and above }\bar{x}-2\sigma \\ 99.7\text{ \% of the distribution lies below }\bar{x}+3\sigma\text{ and above }\bar{x}-3\sigma \end{gathered}[/tex]By symmetry,
[tex]\begin{gathered} 47.5\text{ \% of the distribution lies above }\bar{x}-\sigma\text{ and below }\bar{x} \\ \text{ Hence,} \\ 2.5\text{ \% of the values lies below }\bar{x}-\sigma \end{gathered}[/tex]In our case,
[tex]\bar{x}=14,\sigma=3[/tex]Therefore,
[tex]\begin{gathered} 8=14-6=14-2(3) \\ \text{Hence,'} \\ 8=\bar{x}-2\sigma \end{gathered}[/tex]Hence, 2.5 % of the values lie below 8
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches. Your answer
If Triangle ABC is dilated by a scale factor of 3 and the length of side AB is 15 inches, what is the length of side A'B'? Complete the statement: The length of side A'B' would be inches.
To find out the length side of A'B' multiply the length side AB by the scale factor
so
A'B'=3*(15)=45 inches
Classify each Polynomial by degree and number of terms.1. X^3 + 5x 2. X^2 - 2x - 1 3. 5x^4 4. 6x^5 - 3x^2 + 7x + 9 5. -11x - 5 6. 4x^2 + 10 7. 128. 9x^3 - x^2 + 6x - 1]9. -3x^5 + 6x^4 v- 8THESE ARE THE OPTIONS Degree Name using degree 0 Constant 1 Linear 2 quadratic 3 Cubic 4 quartic 5 quintic 6 6th degreeTHESE ARE ALSO THE OTHER OPTIONSTerms NAME USING # OF TERMS1, monomial 2 , binomial3 trinomial4 or more polynomial
162-317-3113-510Is this relation a function?
can you see my messages?
In a school, 10% of the students have green eyes. Findthe experimental probability that in a group of 4students, at least one of them has green eyes.The problem has been simulated by generating randomnumbers. The digits 0-9 were used. Let the number "9"represent the 10% of students with green eyes. A sampleof 20 random numbers is shown.
Given that in a group of 4 students at least one has green eyes.
Also, the number 9 represents the 10% of the students with green eyes.
From the 20 random experimental numbers given, the number 9 appeared in only nine of them.
The experimental probability in percentage will be:
[tex]\frac{9}{20}\ast100\text{ = }45\text{ percent}[/tex]ANSWER;
45%