ANSWER
[tex]-1[/tex]EXPLANATION
Given;
[tex]\begin{gathered} f(x)=x^2-5x-2 \\ (-1,5) \end{gathered}[/tex][tex]\begin{gathered} f(-1)=(-1)^2-5(-1)-2 \\ =1+5-2 \\ =4 \end{gathered}[/tex]For x = 5;
[tex]\begin{gathered} f(5)=(5)^2-5(5)-2 \\ =25-25-2 \\ =-2 \end{gathered}[/tex]The average is calculated using;
[tex]\begin{gathered} \frac{f(-1)-f(5)}{-1-5} \\ =\frac{4-(-2)}{-1-5} \\ =\frac{6}{-6} \\ =-1 \end{gathered}[/tex]A
for certain workers, the mean wage is $7.00/hr. with a standard deviation of $0.25 . if a worker is chosen at random, what is the probability the worker's wage is between $6.50 and $7.50? assume a normal distribution of wages
The variable of interest is X: earnings of one worker.
This variable has a normal distribution with mean μ=$7.00/hr and standard deviation σ=$0.25
You need to determine the probability that a worker chosen at random earns between $6.50 and $7.50, symbolically:
[tex]P(6.50\leq X\leq7.50)[/tex]To determine the probability within these two values you have to subtract the accumulated probability until 6.50 to the accumulated probability until 7.50:
[tex]P(6.50\leq X\leq7.50)=P(X\leq7.50)-P(X\leq6.50)[/tex]First, you have to determine the corresponding values of the variable under the standard normal distribution, i.e., you have to calculate the Z-values for 7.50 and 6.50:
[tex]Z=\frac{X-\mu}{\sigma}N\sim(0,1)[/tex][tex]P(X\leq7.50)=P(Z\leq\frac{7.50-7}{0.25})=P(Z\leq2)[/tex][tex]P(X\leq6.50)=P(Z\leq\frac{6.50-7}{0.25})=P(Z\leq-2)[/tex]Next, you have to look for the accumulated probability under the standard normal distribution:
[tex]P(Z\leq2)=0.977[/tex]and
[tex]P(Z\leq-2)=0.023[/tex]Now that you have determined the probabilities you can determine the asked one:
[tex]\begin{gathered} P(6.5\leq X\leq7.5)=P(X\leq7.5)-P(X\leq6.5)= \\ P(Z\leq2)-P(Z\leq-2)=0.977-0.023=0.954 \end{gathered}[/tex]There is a 0.954 or 95.4% of probability that the worker choosen at random earns between $6.50/hour and $7.50/hour.
Write each equation in slope intercept formI need it fast please thank you
Answer:
[tex]y(x)=-\frac{6}{5}x-3[/tex]Explanation: The slope-intercept form of the linear equation is the standard form, and is written as follows:
[tex]y(x)=mx+b[/tex]The given equation can be converted into slope-intercept form as follows:
[tex]\begin{gathered} 6x+5y=-15 \\ 5y=-6x-15 \\ y(x)=-\frac{6}{5}x-3 \end{gathered}[/tex]Which number best represents an account balance of S9 below zero?A -490B 19C 490D 49
A number below zero is the same as the negative number.
In this question, an account balance of $49 brelow zero is - 49.
match each trinomial with its correct factorization 1. X'2- 10x - 24. A. (X+8) (x-3)2. X'2 + 11x + 24. B (X+3) (x+8)3. X'2 + 5x - 24. C (x+2) (x-12)4. x'2 + 10x + 24. D (X+24) (X+1)5. X'2 + 25x + 24. E (X+6) (x+4)the 2 next to the X is the exponent by the way.
1.
[tex]\begin{gathered} x^2-10x-24=\mleft(x^2+2x\mright)+\mleft(-12x-24\mright)=x\mleft(x+2\mright)-12\mleft(x+2\mright) \\ =\mleft(x+2\mright)\mleft(x-12\mright) \end{gathered}[/tex]answer: 1 - C
2.
[tex]\begin{gathered} x^2+11x+24=\mleft(x^2+3x\mright)+\mleft(8x+24\mright)=x\mleft(x+3\mright)+8\mleft(x+3\mright) \\ =\mleft(x+3\mright)\mleft(x+8\mright) \end{gathered}[/tex]answer: 2 - B
3.
[tex]\begin{gathered} x^2+5x-24=\mleft(x^2-3x\mright)+\mleft(8x-24\mright)=x\mleft(x-3\mright)+8\mleft(x-3\mright) \\ =\mleft(x+8\mright)(x-3) \end{gathered}[/tex]answer: 3 - A
4.
[tex]\begin{gathered} x^2+10x+24=\mleft(x^2+4x\mright)+\mleft(6x+24\mright)=x\mleft(x+4\mright)+6\mleft(x+4\mright) \\ =\mleft(x+6\mright)(x+4) \end{gathered}[/tex]answer: 4 - E
5.
[tex]undefined[/tex]Determine if 0.1111111111111111...0.1111111111111111... is rational or irrational and give a reason for your answer.
Answer:
Rational
Step-by-step explanation:
Repeating decimals can be expressed as convergent infinite geometric series, which result in fractions of the form p/q, where p and q are coprime positive integers.
Triangle LRG is similar to Triangle CNP. Find the scale factor required to dilate triangle LRG so that its image is is congruent to triangle CNP.
Triangle LRG is similar to triangle CNP. Therefore, the following ratios apply;
[tex]\begin{gathered} \frac{CN}{LR}=\frac{PN}{GR} \\ \text{Similarly,} \\ \frac{CP}{LG}=\frac{PN}{GR} \end{gathered}[/tex]Hence, for triangle LRG to be dilated to become CNP,
[tex]\begin{gathered} \frac{45}{30}=\frac{48}{32} \\ \frac{3}{2}=\frac{3}{2} \end{gathered}[/tex]Therefore, the scale factor needed to dilate triangle LRG so that its image is congruent to triangle CNP is 1.5 (that is the decimal equivalent of 3/2)
This means triangle LRG would be multiplied by 1.5 in order to have an image congruent to triangle CNP
A dice is rolled three times. The first roll is event A, the second roll event B, and the third event C. List below if the events are Independent or Dependent:
Answer:
Independent.
Step-by-step explanation:
An independent event is an event that has no connection to another event's chances of happening. Then for a dice rolled three times, any of the events depends on the other. Hence, all three events are independent.
6) Henry has 4 pints of juice. How many gallons
of juice does Henry have?
If
Answer:
1/2 gallons
Step-by-step explanation:
If 1 gallon is 8 pints, divide 4 pints by 8. This equates to 1/2 gallons.
Add the polynomials (4x2 - 9x + 4) + (7x3 - 9x
we remove the parenthesis and add the number that have the same exponent
[tex]\begin{gathered} 4x^2-9x+4+7x^3-9x \\ 7x^3+4x^2+(-9x-9x)+4 \\ 7x^3+4x^2-18x+4 \end{gathered}[/tex]sporeowner made a list of the number ofred marbles. One marble is selected at random.greeting cards sold last month. The store soldDetermine whether each statement correctly describes the167 thank-you cards, 285 birthday cards andlikelihood of an event based on the given bag of marbles.56 blank cards. Based on this data, what isState whether each statement is True or False.the probability that the next customer willbuy a blank card expressed as a percent?
Given:
A storeowner made a list of number of greeting cards sold last month.
The store sold 167 thank-you cards, 285 birthday cards and 56 blank cards.
Required:
What is the probability that the next customer will buy a blank card expressed as a percent?
Explanation:
We will find total number of cards sold as:
167 + 285 + 56 = 508
Now we will find percentage of each type of card sold as:
[tex]\begin{gathered} Percenatge\text{ of thank you cards sold =}\frac{167}{508} \\ =0.33^\% \end{gathered}[/tex][tex]\begin{gathered} Percentage\text{ of birthday card sold =}\frac{285}{508} \\ =0.56 \end{gathered}[/tex]Percentage of blank cards sold
[tex]\begin{gathered} =\frac{56}{508} \\ =0.11 \end{gathered}[/tex]Answer:
Hence, in percent probability of sold blank card is 11%.
rd
Find the angle of elevation of the sun from the ground, when a tree that is 15yrds tall casts a shadow 17yrds long. Round to the nearest tenth of a degree.
Notice that between the tree (represented by a vertical segment), the ground (represented by a horizontal segment), and the rays of the sun (that go from the top of the tree to the ground), we are in the presence of a right angle triangle that has a short leg of size 15 yards (verticel segment), and a long leg of size 17 yards.
Then the angle of elevation is assicuated with the tangent function in that right angle triangle:
[tex]\tan (\alpha)=\frac{15}{17}[/tex]This is the quotient of the side opposite to the angle divided the side adjacent to the angle. Then we can solve for the angle by using the arctangent the following way:
arctan(15/17) (this is what you type in your calculator, but make sure your answer comes in DEGREES. (you need to set your calculator for that)
As I do it in my calculator, I get that the angle is: 41.42366 degrees
And since they want us to round it to the nearest tenth, we give:
angle of elevation = 41.4 degrees.
a) Determine if the triangles are similar.b) If they are similar write the reason. (SSS, SAS, AA, NONE)c) The red segments are called...____(medians, heights, perpendicular bisectors, angle bisectors)d) ×=
Answer:
• a. Yes
,• b. SAS
,• c. Height
,• d. x=14
Explanation:
Part A
The two triangles have an angle of 76 degrees at the altitudes U and F respectively.
Similarly, the ratio of their corresponding sides are:
[tex]\begin{gathered} \frac{WU}{HF}=\frac{9}{21}=\frac{3}{7} \\ \frac{UV}{FG}=\frac{18}{42}=\frac{3}{7} \end{gathered}[/tex]Part B
We conclude that:
Triangle HFG is similar to triangle WUV by the SAS congruence Theorem.
Part C
The red segments are called heights of the triangles.
Part D
The ratio of corresponding sides = 3/7
Thus:
[tex]\begin{gathered} \frac{6}{x}=\frac{3}{7} \\ 3x=6\times7 \\ x=\frac{6\times7}{3} \\ x=14 \end{gathered}[/tex]A real estate broker earns a fixed percentage of the selling price of a house as a commission. The broker sold a house for $ 278,000 and earned a commission of $ 16,680. What would the broker's commission be on a house that sells for $ 324,000?
first, we find the percentage of the commission earned:
$278,000 ----> 100%
$16,680 ------> x
then solve
[tex]\begin{gathered} 278000\cdot x=16680\cdot100 \\ 278000x=1668000 \\ \frac{278000x}{278000}=\frac{1668000}{278000} \\ x=6 \end{gathered}[/tex]therefore the commission is 6%. So,
$324,000 ------> 100%
y -------------------> 6%
[tex]\begin{gathered} y\cdot100=324000\cdot6 \\ 100y=1944000 \\ \frac{100y}{100}=\frac{1944000}{100} \\ y=19440 \end{gathered}[/tex]answer: $ 19,440
13 students is. % of 25 students
In order to find the percentage that 13 represents from 25, we can use the following rule of three, knowing that 25 students represent 100%:
[tex]\begin{gathered} 25\text{ students}\to100\text{\%} \\ 13\text{ students}\to x\text{\%} \\ \\ \frac{25}{13}=\frac{100}{x} \\ 25x=13\cdot100 \\ x=\frac{1300}{25} \\ x=52 \end{gathered}[/tex]So 13 students is 52% of 25 students.
How much fabric is needed for a round tablecloth if the radius of the table is 8 inches?
We have to calculate the area of the table:
Area of a circle:
π x radius^2
Give
-17=3+5x helpppppppppppppppppppp
Answer: x=4
Step-by-step explanation:
add common terms to one side then divide
given equation
-17 = 3 + 5x
5x =3 + 17
5x = 20
x = 20/5
x = 4
A chef bought $17.01 worth of ribs and chicken. Ribs cost 1.89 per pound and chicken costs 0.90 per
pound. The equation 0.90 +1.89r = 17.01 represents the relationship between the quantities in this
situation.
Show that each of the following equations is equivalent to 0.9c + 1.89r = 17.01. Then, explain when
it might be helpful to write the equation in these forms.
a. c=18.9-2.1r. b. r= -10÷2c+9
Answer: c=18.9-2.1r.
Step-by-step explanation:
Answer:
Step-by-step explanation:
we have that
The linear equation in standard form is
where
c is the pounds of chicken
r is the pounds of ribs
Solve the equation for c
That means ----> isolate the variable c
Subtract 1.89r both sides
Divide by 0.90 both sides
Simplify
Solve the equation for r
That means ----> isolate the variable r
Subtract 0.90c both sides
Divide by 1.89 both sides
Simplify
therefore
The equation is equivalent
The equation is helpful, because if I want to know the number of pounds of chicken, I just need to substitute the number of pounds of ribs in the equation to get the result.
Ana mixed together 3 gallons of Brand A orange juice and 2 gallons of Brand B orange juice. Brand B orange juice contains 64% fruit juice. What is the percent of fruit juice in Brand A if the mixture contains 49% fruit juice? A) 36% B) 39% C 51% D 57%
Mixture
5 gal 48% fruit juice contains
[tex]5\times\frac{49}{100}=2.45\text{ gal pure juice}[/tex]From brand B,
[tex]2\times\frac{64}{100}=1.28\text{ gal juice}[/tex]Therefore, pure juice from brand A is,
[tex]\begin{gathered} 2.45-1.28=1.17 \\ \end{gathered}[/tex]therefore percentage is,
[tex]\frac{1.17}{3}\times100=39[/tex]please can you tell me if 7 question answer is right
In the image above you have the distribution of the 16 seats in the van (in pairs). You can identify the number of pairs (two seats) in red.
Then, there are 8 pair of seats3 1/2 x 3 1/2 I need the answer
Answer:
Your answer is [tex]12.25[/tex] or [tex]12 \frac{1}{4}[/tex]
Step-by-step explanation:
[tex]3.5[/tex] × [tex]3.5 = 12.25[/tex]
The line in the coordinate grid passes through points (-2, -5) and (4, 4).
If the equation of this line is written in the slope-intercept form , what is the value of ?
Answer:
m is slope = (9/6)
b isy-intercept = -2
Step-by-step explanation:
I will assume that "the value of ?" is meant to read "the value of m?."
The slope-intercept form of a line is y = mx + b, where m is the slope of b is the y-intercept (the value of y when x = 0).
We can caluclate slope from the two given points. Slope is the "Rise/Run" of a line. [The change in y for a change in x].
The two points (-2,-5) and (4,4) can be uysed to calculate the slope.
Rise is the change in y: (4 - (-5)) = 9 [the value of y increased by 9].
Run is the change in x: (4 - (-2)) = 6 [x increased by 6].
Slope is the Rise/Run: (9/6)
This tells us that the rate of change between these points is (9/6). Every change in 6 x units will creat a change of + 9 y units.
The equation for the line connecting these 2 points becomes:
y = (9/6)x + b
In the even the question is looking for the value of b, we can calculate b by entering one of the two points in the equation above:
y = (9/6)x + b
y = (9/6)x + b [for (4,4)]
4 = (9/6)*4 + b
4 = 6 + b
b = -2
The equation connecting thses 2 points is y = (9/6)x - 2
See attached graph
Draw the graph of -3 times f(x) where f(x)=cosx And give it's period
It is required to draw the graph of -3f(x), where f(x)=cos x.
It is also required to give its period.
To do this, start with the graph of the parent function f(x)=cos x, then perform transformations on the graph of the parent function to draw the required graph.
The graph of the parent function f(x)=cos x is shown below:
Reflect the graph over the x-axis to draw the graph of -f(x) (in blue):
Stretch the graph of -f(x) vertically by a factor of 3 to draw the graph of -3f(x) (in green):
The required graph of -3f(x) is:
Recall that the period of a sinusoid is the length of a complete cycle.
From the graph, the period is 2π.
Ryan enjoys flying a kite on the beach.Which is closest to the length of the string?
Answer:
184ft
Explanation:
To be able to determine the length of the string, we have to find the length of the hypotenuse side of the triangle.
Let the length of the hypotenuse be x.
To find x, we have to take the cosine of angle 57;
[tex]\begin{gathered} \cos 57=\frac{100}{x} \\ x\cos 57=100 \\ x=\frac{100}{\cos 57} \\ x=184ft \end{gathered}[/tex]Figure ABCD has an area of 4 units^2. It is thendilated using a scale factor of 4. What is theperimeter of the new figure?A.) 8B.) 32C.) 64
We have the following:
We can see that the side of the square ABCD is 2, but if we apply the scale factor it will be:
[tex]l=2\cdot4=8[/tex]We know that the perimeter is the sum of all the sides, therefore it would be
[tex]\begin{gathered} p=8+8+8+8 \\ p=32 \end{gathered}[/tex]Which means that the correct option is B.) 32
Solve the system of equations using elimination. −2x + 3y = 15 x + y = 10
Answer:
[tex]x=3[/tex]
[tex]y=7[/tex]
Step-by-step explanation:
[tex]-2x+3y=15\\[/tex] (1)
[tex]x+y=10[/tex] (2)
Multiply equation (2) by 2:
[tex]2x+2y=20[/tex]
Add this new equation to equation (1):
[tex]5y=35[/tex]
Divide both sides by 5:
[tex]y=7[/tex]
Substitute this value for 7 into either original equation:
[tex]x+7=10[/tex]
Solve:
[tex]x=3[/tex]
I am on the roof of a 1200ft building, and I am looking at an even taller skyscraper. I have an inclinometer. WhenI look up at the top of the skyscraper, my inclinometer reads that I am looking up at an angle of elevation of35 degrees above the horizontal. When I look down at the base of the skyscraper, my inclinometer reads that Iam looking down at an angle of depression of 60 degrees below the horizontal. I also know that the building andskyscraper are 600 ft apart. Find the height of the skyscraper in exact and approximate form.
Let's try to draw a rough diagram of the problem:
From here, we can dissect a triangle as shown below:
From this diagram, we are going to find H, the height of the skyscraper.
We already know that part of the side length "H" is 1200 feet. We need to find the other part of "H". Let's label it h1.
Finding h1:
[tex]\begin{gathered} \tan 35=\frac{h1}{600} \\ h1=600\tan 35 \\ h1=420.12 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} H=h1+1200 \\ H=420.12+1200 \\ H=1620.12 \end{gathered}[/tex]The height of the skyscraper is 1620.12 feet
Can someone please help?
Answer:
< SRT and < POR
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y = (-3/2)x - 14?
The line is given by y=(-3/2)x-14.
The general equation of a straight line is y=mx+c, where m is the slope and c is the y intercept.
Comparing y=(-3/2)x-1 with y=mx+c, we find that the slope is m=-3/2.
The slope of a line that is perpendicular to the line with slope m is ,
M=-(1/m)
Hence, the slope of the perpendicular line is,
[tex]M=-\frac{1}{m}=\frac{-1}{\frac{-3}{2}}=\frac{2}{3}[/tex]Therefore, the slope of a line that is perpendicular to the line y = (-3/2)x - 14 is 2/3.
∠1 and ∠2 are vertical angles. m∠1 = 40° and m∠2 = (7x + 5)°.
The value of x is 5°.
Given:
∠1 and ∠2 are vertical angles, m∠1 = 40° and m∠2 = (7x + 5)°.
Vertical angles are angles that are opposite to each other and by definition these angles are congruent or equal.
That is m∠1 and m∠2 are equal.
m∠1 = m∠2
40 = (7x + 5)
7x = 40 - 5
7x = 35
divide by 7 on both sides we get
7x/7 = 35/7
x = 35/7
x = 5°.
Therefore the value of x is 5°.
Learn more about the value and vertical angles here:
https://brainly.com/question/23087234
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Write each of the following as an algebraic expression-The complement of a angle measuring 2x+3 degrees
Two angles are complementary if they add up to 90 degrees.
Let the complement of the angle measuring 2x+3 degrees = y
Therefore:
[tex]\begin{gathered} y+(2x+3)^0=90^0 \\ y=90^0-(2x+3)^0 \end{gathered}[/tex]Therefore, the complement of an angle measuring (2x+3) degrees is:
[tex]90^0-(2x+3)^0[/tex]