The function is:
[tex]f(x)=3x^2-2x+1[/tex]to check witch is true we have to evaluate the function in -1, 1, 1 and 0 so:
for
Determine the transformations that produce the graph of the functions g (T) = 0.2 log(x+14) +10 and h (2) = 5 log(x + 14) – 10 from the parent function f () = log 1. Then compare the similarities and differences between the two functions, including the domain and range. (4 points)
The transformation to get g(x) from f(x) are:
translate 14 units to the left and 10 unit upwards
[tex]h(x)=5\log (x+14)-10[/tex]the transformatio to get h(x) from f(x) are:
translate 14 units to the left and 10 units downwards
LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit
The Solution:
Given the graph below:
We are required to find the perimeter of the triangle LMN rounded to the nearest unit.
Step 1:
Find the distance LM, where L(-3,2) and M(3,5)
By the formula for distance between two points, we have
[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]Substituting, we get
[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]Step 2:
Find the distance LN:
[tex]LN=12[/tex]Step 3:
Find the distance MN, where M(3,5) and N(9,2)
[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]Step 4:
The perimeter is:
[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]Therefore, the correct answer is 28 units.
Expand and simplify 3(3x - 4) - 2(2x - 1)
Answer:
5x-10
Step-by-step explanation:
expand to 9x-12-4x+2
collect like terms.
5x-10
13х-17y+16z= 73
-11x + 15y + 17z= 61
46x+10y-30z = -18
The solution of the linear system of three simultaneous equations is presented as follows; x = 2, y = 1 and z = 4
What is a set of simultaneous equation?Simultaneous system of equations consists of a finite set of equations for which a solution to the equation system is required.
The linear system of three equations can be presented as follows;
13•x - 17•y + 16•z = 73...(1)
-11•x + 15•y + 17•z = 61...(2)
46•x + 10•y - 30•z = -18...(3)
The above system of equations can be solved using common multiples of the coefficients as follows;
Multiply equation (2) by 2 and equation (3) by 3 to get;
2 × (-11•x + 15•y + 17•z) = 2 × 61 = 122
-22•x + 30•y + 34•z = 122...(4)3 × (46•x + 10•y - 30•z) = 3 × (-18) = -54
138•x + 30•y - 90•y = -54...(5)Subtracting equation (4) from equation (5) gives;
138•x + 30•y - 90•z - (-22•x + 30•y + 34•z) = -54 - 122 = -176
138•x - (-22•x) + 30•y - 30•y - 90•z - 34•z = -176
160•x - 124•z = -176
40•x - 31•z = 44
[tex] \displaystyle {z = \frac{(44 + 40\cdot x)}{31}}[/tex]
Plugging in the value of z in equation (1) and (2) gives;
1043•x - 527•y + 704 = 73 × 31 = 2236...(6)
Which gives;
[tex] \displaystyle {y = \frac{(1043\cdot x - 1559)}{527}}[/tex]
339•x + 465•y + 748 = 61 × 31 = 1891...(7)
Which gives; [tex] \displaystyle {y = \frac{(381 - 113\cdot x )}{155}}[/tex] which gives;
[tex] \displaystyle { \frac{(1043\cdot x - 1559)}{527}= \frac{(381 - 113\cdot x )}{155}}[/tex]
Therefore; 221216•x - 442432 = 0
x = 442432 ÷ 221216 = 2
x = 2
y = (1043×2 - 1559)÷527 = 1
y = 1
z = (44 + 40×2) ÷ 31 = 4
z = 4
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A baker has 85 cups of flour to make bread. She uses 6 1/4 cups of flour for each loaf of bread. How many loaf of bread can she make
Answer;
The number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]Explanation:
Given that a baker has 85 cups of flour to make bread.
[tex]A=85\text{ cups}[/tex]And for each bread she uses 6 1/4 cups of flour.
[tex]r=6\frac{1}{4}\text{ cups}[/tex]The number of loaf of bread she can make can be calculated by dividing the total amount of flour by the amount of flour per bread;
[tex]\begin{gathered} n=\frac{A}{r}=\frac{85}{6\frac{1}{4}}=\frac{85}{6.25} \\ n=13.6 \end{gathered}[/tex]Since it will not complete the 14th loaf of bread.
So, the number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]Find the 11th term of the arithmetic sequence -5x- 1, -8x + 4, -11 x+ 9, ...
Recall that an arithmetic sequence is a sequence in which the next term is obtained by adding a constant term to the previous one. Let us consider a1 = -5x-1 as the first term and let d be the constant term that is added to get the next term of the sequence. Using this, we get that
[tex]a_2=a_1+d[/tex]so if we replace the values, we get that
[tex]-8x+4=-5x-1+d[/tex]so, by adding 5x+1 on both sides, we get
[tex]d=-8x+4+5x+1\text{ =(-8+5)x+5=-3x+5}[/tex]To check if this value of d is correct, lets add d to a2. We should get a3.
Note that
[tex]a_2+d=-8x+4+(-3x+5)=-11x+9=a_3[/tex]so the value of d is indeed correct.
Now, note the following
[tex]a_3=a_2+d=(a_1+d)+d=a_1+2d=a_1+d\cdot(3-1)[/tex]This suggest the following formula
[tex]a_n=a_1+d\cdot(n-1)[/tex]the question is asking for the 11th term of the sequence, that is, to replace the value of n=11 in this equation, so we get
[tex]a_{11}=a_1+d\cdot(10)=-5x-1+10\cdot(-3x+5)\text{ =-5x-1-30x+50 = -35x+49}[/tex]so the 11th term of the sequence is -35x+49
18. The weights of four puppies are shown in pounds. 9.5 9 9.125 9 Which list shows these weights in order from greatest to least F. 99.5 9 9.125 w 9.5 9 9.125 9.125 9 9.5 9 + J. 9 9 9.5 9.125
The correct list is
[tex]9\frac{3}{4},\text{ 9.5, 9}\frac{3}{8},9.125[/tex]This is option F
Why is it incorrect to write {∅} to denote a set with no elements?
Answer:
It's incorrect because {∅} is saying that the set contains empty sets, which is not the same as saying the set is empty (which can be denoted by { } or ∅
Step-by-step explanation: It's all in the answer.
Determine if the side lengths could form a triangle. Use an inequality to prove the answer. Inequality must be used.
The side lengths given form a triangle
Explanation:Let the lengths of the sides of the triangle be "a", "b" and "c"
For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:
[tex]\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}[/tex]Given the sides of the triangle as 34km, 27km, and 58km
Let a = 34km, b = 27km and c = 58km
Substituting these values in the expression above to check if it is true:
[tex]\begin{gathered} 34+27=61>58 \\ 34+58=92>27 \\ 27+58=85>34 \end{gathered}[/tex]Since the inequality expression supports the theorem above, hence the side lengths given form a triangle
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
Find the slope, if it exists, of the line containing the pair of points. (−2,−6) and (−15,−7)
The linear regression for a given data set has the form
[tex]y=a+bx[/tex]where the values a and b can be solved using the equation
[tex]\begin{gathered} a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2} \\ b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2} \end{gathered}[/tex]Based on the given data set, we have n equals 5. We will solve for the values of the summation first. We have the following
[tex]\begin{gathered} \sum y=4+4+6+6+8=28 \\ \sum x=1+3+5+7+9=25 \\ \sum xy=(1\cdot4)+(3\cdot4)+(5\cdot6)+(7\cdot6)+(8\cdot9)=160 \\ \sum x^2=1^2+3^2+5^2+7^2+9^2=165^{} \\ (\sum x)^2=25^2=625 \end{gathered}[/tex]Using these values to compute for the values of a and b, we get
[tex]\begin{gathered} a=\frac{(28\cdot165)-(25\cdot160)}{5(165)-625}=\frac{31}{10}=3.1 \\ b=\frac{5(160)-(28\cdot25)}{5(165)-625}=\frac{1}{2}=0.5 \end{gathered}[/tex]Take note that the problem wants us to reduce the numbers to the nearest tenth. Hence, the linear regression for the given data set is written as
[tex]y=3.1+0.5x[/tex]You pick a card at random.
1 2 3 4
What is P(factor of 24)?
Write your answer as a percentage rounded to the nearest tenth
Answer:
100%
Step-by-step explanation:
All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.
This is equal to 100%.
Match the following. Match the items in the left column to the items in the right column.1. divisor2. decimal fraction3. algorithm4. fraction5.quotient6. reminder7. doidonsa. the result of dividing two numbersb. the number being dividedc. a set of rules to be followed tosolve a problemd. the number of equal parts a number is being divided intoe. a fraction in which the denominator is 10 or a power of 10f. the amount left over after Chivisiong. a number that expresses the portiona whole
We can match as follows:
1. divisor ----> d. the number of equal parts a number is being divided into
2. decimal fraction ----> e. a fraction in which the denominator is 10 or a power of 10
3. algorithm ----> c. a set of rules to be followed to solve a problem
4. fraction ----> g. a number that expresses the portion
5. quotient ----> a. the result of dividing two numbers
6. reminder ----> f. the amount left over after Division
Rewrite 25% as a fraction in simplest form.
Answer:
1/4
Step-by-step explanation:
use the above diagram to answer the following questions.
Remember that the sum of the interior angles is 180. Then, we have the following equation:
[tex]55^{\circ}+65^{\circ}\text{ + }\angle M\text{ = 180}[/tex]This is equivalent to:
[tex]120^{\circ}\text{ + }\angle M=180^{\circ}[/tex]solve for M-angle:
[tex]\text{ }\angle M=180^{\circ}-\text{ 120}^{\circ}=60^{\circ}[/tex]Then, te correct answer is :
[tex]\text{ }\angle M^{}=60^{\circ}[/tex]how many term has G.p whose 2nd term is 1/2 and common ratio and the last term are 1/4and1/128respestively
The geometric progression has the form:
[tex]\mleft\lbrace a,ar,ar^2,ar^3,\ldots,ar^n\mright\rbrace[/tex]We have the information about the second term, a*r:
[tex]ar=\frac{1}{2}[/tex]We know that the common ratio is
[tex]r=\frac{1}{4}[/tex]So from this information we can get the coefficient a:
[tex]\begin{gathered} ar=\frac{1}{2} \\ a\cdot\frac{1}{4}=\frac{1}{2} \\ a=\frac{4}{2}=2 \end{gathered}[/tex]And we also know that the last term is 1/128, that is
[tex]ar^n=\frac{1}{128}[/tex]From this one we can find n:
[tex]\begin{gathered} 2\cdot(\frac{1}{4})^n=\frac{1}{128} \\ (\frac{1}{4})^n=\frac{1}{128\cdot2} \end{gathered}[/tex]We can apply the property of the logarithm of power to get n:
[tex]\begin{gathered} \log ((\frac{1}{4})^n)=\log (\frac{1}{256}) \\ n\cdot\log (\frac{1}{4})^{}=\log (\frac{1}{256}) \\ n=\frac{\log (\frac{1}{256})}{\log (\frac{1}{4})} \\ n=4 \end{gathered}[/tex]Be careful, because n is not the number of terms. The number of terms is n+1, so the G.P. has 5 terms
In a survey, 12 people were asked how much they spent on their child's last birthday gift. The results wereroughly bell-shaped with a mean of $39.1 and standard deviation of $17.4. Estimate how much a typical parentwould spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.Express your answer in the format of ī + Error.$£ $
Given:
number of people (n) = 12
mean = 39.1
standard deviation = 17.4
99% confidence level
Using the confidence level formula, we can find the estimate of how much a typical parent would spend on their child's birthday:
[tex]\begin{gathered} CI\text{ = x }\pm\text{ }\frac{z\varphi}{\sqrt[]{n}} \\ \text{where x is the mean} \\ z\text{ is the z-score at 99\% confidence interval} \\ \varphi\text{ is the standard deviation} \\ n\text{ is the number of people asked} \end{gathered}[/tex]The z-score at 99% confidence level is 2.576
Substituting, we have:
[tex]\begin{gathered} CI\text{ = 39.1 }\pm\text{ }\frac{2.576\text{ }\times\text{ 17.4}}{\sqrt[]{12}} \\ =26.161\text{ and 52}.039 \end{gathered}[/tex]Hence, a typical parent would spend between $26.161 and $52.039 or :
[tex]39.1\text{ }\pm\text{ 12.939}[/tex]30 randomly selected students took the statistics final. If the sample mean was 84, and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students
The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}
What is confidence interval?Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.
How to construct a 99% confidence intervalGiven data form the question
99% confidence interval
30 randomly selected students
mean sample = 84
Standard deviation = 12.2
Definition of variables
confidence level, CI = 99%
mean sample, X = 84
standard deviation, SD = 12.2
Z score, z = 2.576
from z table z score of 99%confidence interval = 2.576sample size, n = 30
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]
=[tex]=84+2.576*2.2274[/tex]
= 84 + 5.7378 OR 84 - 5.7378
= 89.7378 OR 78.2622
= 89.73 to 78.26
The confidence interval for the mean score of all students is 78.26 to 89.78
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a large human population of both globally and within individual countries has been a concern since the time of Thomas Malthus. country X is 95% desert. the government of country X is concerned about not having enough arable land (land capable of being used to grow crops) in the country to produce the food needed to feed its population without increasing food imports the demographic for Country X for the year 2020 is provided in the table below. 1. calculate the national population growth rate for a country X 2. using the rule of 70 calculate the doubling time for this population
Firstly, we want to calculate the growth rate of the population
While birth would increase the population, death and migration will decrease the population
So when we subtract the migration rate and the death rate from the birth rate, we can get the population growth rate;
Thus, we have;
[tex]\begin{gathered} \frac{38}{1000}\text{ - (}\frac{24}{1000}\text{ + }\frac{2}{1000}) \\ \\ =\text{ }\frac{38}{1000}\text{ - }\frac{26}{1000} \\ \\ =\text{ }\frac{12}{1000} \end{gathered}[/tex]The national population growth rate for a country X is 12/1000
Secondly, we are to use the rule of 70 to calculate the doubling time for the population
Mathematically;
[tex]\begin{gathered} No\text{ of years to double = }\frac{70}{\text{annual growth rate}} \\ \\ No\text{ of years to double = 70 divided by }\frac{12}{1000} \\ \\ No\text{ of years = 70 }\times\frac{1000}{12}=5833\frac{1}{3}years^{} \\ \\ \frac{1}{3}\text{ years is same as 4 months} \\ \\ So\text{ it will take 5833 years and 4 months for the population to double} \end{gathered}[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
If 16 is increased to 23, the increase is what percent of the original number? (This is known as the percent of change.)
Step 1
Given data
Old value = 16
New value = 23
Step 2
Write the percentage increase formula
[tex]\text{Percentage increase = }\frac{I\text{ncrease}}{\text{Old}}\text{ }\times\text{ 100\%}[/tex]Step 3
Increase = 23 - 16 = 7
[tex]\begin{gathered} \text{Percentage increase = }\frac{7}{16}\text{ }\times\text{ 100\%} \\ =\text{ 43.75\%} \end{gathered}[/tex]Malachi is making a fruit smoothie. In addition to a frozen banana, he wants to add one other fruit and one small container of yogurt.
If he has four different options for fruit (blueberries, strawberries, peaches, and raspberries) and three different options for yogurt flavors (plain, vanilla, and lemon), how many fruit smoothie combinations are possible?
There are
possible fruit smoothie combinations.
Answer:
12 different combinations are possible (I think)
Step-by-step explanation:
Let's try to understand,
1. Blueberries + Plain Yogurt
2. Strawberries + Plain Yogurt
3. Peaches+ Plain Yogurt
4. Raspberries + Plain Yogurt
5. Blueberries + Vanilla Yogurt
6. Strawberries +VanillaYogurt
7. Peaches+ VanillaYogurt
8. Raspberries + VanillaYogurt
9. Blueberries + Lemon Yogurt
10. Strawberries + Lemon Yogurt
11. Peaches+ Lemon Yogurt
12. Raspberries + LemonYogurt
I hope this is the right answer and if not please forgive.
A disk is in the form of square and measures 5.25inches on each side. Find the diagonal length of thedisk. I am taking geometry In the 8th grade and I am lost
Answer:
The diagonal length is 7.42 inches.
Explanation:
The disk with its diagonal is:
Then, we can look at the diagonal as the hypotenuse of a right triangle. Then, if we call D to the diagonal:
[tex]\begin{gathered} D^2=(5.25in)^2+(5.25)^2 \\ D=\sqrt{2(5.25in)^2}\approx7.42in \end{gathered}[/tex]i need help please and thank youthere are 2 pictures bc i couldn’t get it all in 1!
we have the system
y < -2x^2+4x-2
The solution for this inequality is the shaded area below the vertical dashed parabola
and
[tex]y\ge\frac{2}{3}x-3[/tex]the solution for this inequality is the shaded area above the solid line y=(2/3)x-3
therefore
the solution for this system of inequalities
Is the shaded area below the vertical dashed parabola y=-2x^2+4x-2 and above the solid line y=(2/3)x-3
see the attached figure to better understand the problem
how would u decide if 3/5 or 59% is greater?
SOLUTION
Step 1 : One of the easiest ways to determine which one of the quantities is greater is by expressing the quantities as a decimal.
[tex]\begin{gathered} \frac{3}{5}\text{ = 0.6} \\ \\ 59\text{ \% = 0.59} \end{gathered}[/tex]Step 2: From the two quantities expressed as decimals, we can see that :
[tex]\frac{3}{5}\text{ is greater.}[/tex]CONCLUSION :
[tex]\frac{3}{5}\text{ is greater.}[/tex]A) Write an expression for the given number trick B) Simplify the expression you came up with
a)
Since we need an Expression, we also need a variablel for the "number".
Let's use "n".
We will translate each of the lines:
Pick a number : n
Mutiply that number by 12, so it becomes: n x 12
Add 15 to that, so we put parenthesis around that expression and add "15" to it:
(n x 12) + 15
Divide by 3, then we simply divide whole thing by 3, so we have:
[tex]\frac{(n\times12)+15}{3}[/tex]b)
To simplify, let's re-write:
[tex]\begin{gathered} \frac{(n\times12)+15}{3} \\ =\frac{12n+15}{3} \\ =\frac{12n}{3}+\frac{15}{3} \\ =4n+5 \end{gathered}[/tex]This is the simplified form.
what is the sum of -1 1/3 + 3/4
Here, we want to add two fractions
What we have to do here is to make the mixed fractin an improper one
To do this, we multiply the denominator by the standing number, and add to the numerator, then we place the value over the denominator
Thus, we have it that;
[tex]\begin{gathered} 1\frac{1}{3}\text{ = }\frac{4}{3} \\ -\frac{4}{3}+\frac{3}{4}\text{ = }\frac{-16+9}{12}=\text{ }\frac{-7}{12} \end{gathered}[/tex]Do 9 and 10 keep it 9th grade if you can Question 9-10
Given the formula for the volume of a cylinder:
[tex]V=\pi r^2h[/tex]You know that "r" is the radius of the cylinder and "h" is the height.
a. In order to solve the formula for "h", you can divide both sides of the formula by:
[tex]\pi r^2[/tex]As follows:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{V}{\pi r^2}[/tex]b. Having a cylindrical swimming pool, you know that:
[tex]\begin{gathered} r=12\text{ }ft \\ V=1810\text{ }ft^3 \end{gathered}[/tex]And, for this case:
[tex]\pi\approx3.14[/tex]Therefore, you can substitute values into the formula for the height of a cylinder found in Part "a" and evaluate:
[tex]\frac{V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{(3.14)(12\text{ }ft)^2}[/tex][tex]h=\frac{1810\text{ }ft^3}{452.16\text{ }ft^2}[/tex][tex]h\approx4\text{ }ft[/tex]Hence, the answers are:
a.
[tex]h=\frac{V}{\pi r^2}[/tex]b.
[tex]h\approx4\text{ }ft[/tex]The function C(x) =17.5x-10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon.
a) It represents the discount of $10 coupon
b) It repesetns the cost of each ticket
c) Five tickets cost is:
C(5) = 17.5(5) - 10 = 87.5 - 10 = 77.5
Five tickets cost $77.50
d) 130 = 17.5x - 10
130 + 10 = 17.5x
140 = 17.5x
x = 140/17.5 =8
x = 8
With $130 you can buy 8 tickets
Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 17 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 112 million dollars? Round your answer to four decimal places.
0.8413 is the probability that a random selected firm will earn less than 112 million dollar
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Let X be a random variable represents the income of the firm in the industry
Hence
X~ N (mean =u= 95 , standard deviation= d = 17 )
We must determine the likelihood that a randomly chosen company will make fewer than 112 million dollars in earnings ie.
P(X<112) = P(X-u/d < 112-95/17)
Z=X-u/d = 112 - 95/17 = 1
P(X<112) = P(Z-1)=0.8413
Using the standard normal probability table.
P(X<112) = 0.8413
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