Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
Red maple trees can reach heights up to 80 feet. What is the height of the maple tree shown below?
Answer:
h = 54.5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 35 = h/95
95 sin 35 = h
h=54.48976
Rounding to the nearest tenth
h = 54.5
Answer:
Step-by-step explanation:
[tex]sin 35/h = sin 90/95\\n=54.48976145\\54.5[/tex]
Consider the piecewise function shown on the graph, which is composed of three different function types. ----- IMAGE ATTACHED BELOW
Match each piece of the function with its domain.
Answer:
[tex]Domain = (-\infty,-2)[/tex] --- quadratic function
[tex]Domain = (-2,6)[/tex] --- linear function
[tex]Domain = (6,\infty)[/tex] --- square root function
Step-by-step explanation:
Given
The attached graph
Required
The domain of each function
Starting from the left; the first function is the quadratic function.
The curve of the quadratic function stops at -2 So, the domain is:
[tex]Domain = (-\infty,-2)[/tex]
The straight line that starts at -2 and ends at 6 is a linear function.
So, the domain is:
[tex]Domain = (-2,6)[/tex]
Lastly, the square root function begins at 6. So, the domain is:
[tex]Domain = (6,\infty)[/tex]
Answer:
quadratic = (-∞,-2)
square root = (6,∞)
linear = (-2,6)
Step-by-step explanation:
Coordinate plane with quadrilaterals EFGH and E prime F prime G prime H prime at E 0 comma 1, F 1 comma 1, G 2 comma 0, H 0 comma 0, E prime negative 1 comma 2, F prime 1 comma 2, G prime 3 comma 0, and H prime negative 1 comma 0. F and H are connected by a segment, and F prime and H prime are also connected by a segment. Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilations compares segment F'H' to segment FH
Answer:
[tex]|F'H'| = 2 * |FH|[/tex]
Step-by-step explanation:
Given
[tex]E = (0,1)[/tex] [tex]E' = (-1,2)[/tex]
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]G = (2,0)[/tex] [tex]G' =(3,0)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
[tex](x,y) = (1,0)[/tex] -- center
[tex]k = 2[/tex] --- scale factor
See comment for proper format of question
Required
Compare FH to F'H'
From the question, we understand that the scale of dilation from EFGH to E'F'G'H is 2;
Irrespective of the center of dilation, the distance between corresponding segment will maintain the scale of dilation.
i.e.
[tex]|F'H'| = k * |FH|[/tex]
[tex]|F'H'| = 2 * |FH|[/tex]
To prove this;
Calculate distance of segments FH and F'H' using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Given that:
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
We have:
[tex]FH = \sqrt{(1- 0)^2 + (1- 0)^2}[/tex]
[tex]FH = \sqrt{(1)^2 + (1)^2}[/tex]
[tex]FH = \sqrt{1 + 1}[/tex]
[tex]FH = \sqrt{2}[/tex]
Similarly;
[tex]F'H' = \sqrt{(1 --1)^2 + (2 -0)^2}[/tex]
[tex]F'H' = \sqrt{(2)^2 + (2)^2}[/tex]
Distribute
[tex]F'H' = \sqrt{(2)^2(1 +1)}[/tex]
[tex]F'H' = \sqrt{(2)^2*2}[/tex]
Split
[tex]F'H' = \sqrt{(2)^2} *\sqrt{2}[/tex]
[tex]F'H' = 2 *\sqrt{2}[/tex]
[tex]F'H' = 2\sqrt{2}[/tex]
Recall that:
[tex]|F'H'| = 2 * |FH|[/tex]
So, we have:
[tex]2\sqrt 2 = 2 * \sqrt 2[/tex]
[tex]2\sqrt 2 = 2\sqrt 2[/tex] --- true
Hence, the dilation relationship between FH and F'H' is::
[tex]|F'H'| = 2 * |FH|[/tex]
Answer:NOTT !! A segment in the image has the same length as its corresponding segment in the pre-image.
Step-by-step explanation:
An absolute value function has
A. Curved lines that only increases and decreases.
B. Straight lines that do both increase ,decrease, or stay constant on the same graph
C.Straight line that do both increase and decrease on the same graph
D. Straight lines that only increase or decrease
E. Curved lines that do both increase and decrease on the same graph
Which of the following pairs of functions are inverses of each other?
O A. f(x) = 2x–9 and g(x) = *7 9
B. f(x)=$+4 and g(x) = 3x-4
C. f(x)=5+*fx and g(x) = 5 - 43
O D. f(x) = 3-6 and g(x) = x26
Answer:
I think its B
Step-by-step explanation:
The pairs of functions which are inverses of each other is A. f(x) = 2x - 9 and g(x) = (x + 9)/2.
What is Inverse Function?Inverse functions are functions which can be reversed in to another function.
Then the function is said to be the inverse of the second function.
If two functions f(x) and g(x) are inverses of each other, then f(g(x) = x and g(f(x)) = x.
A. f(x) = 2x - 9 and g(x) = (x + 9)/2
f(g(x)) = f((x + 9)/2) = 2 [(x + 9)/2] - 9 = x + 9 - 9 = x
g(f(x)) = g(2x - 9) = (2x - 9 + 9) / 2 = 2x / 2 = x
So, the functions are inverses of each other.
B. f(x) = (x/3) + 4 and g(x) = 3x - 4
f(g(x)) = f(3x - 4) = [(3x - 4)/3] + 4 ≠ x
So not inverses of each other.
C. f(x) = 5 + ∛x and g(x) = 5 - x³
f(g(x)) = f(5 - x³) = 5 + ∛(5 - x³) ≠ x
So not inverses of each other.
D. f(x) = (2/x) - 6 and g(x) = (x + 6)/2
f(g(x)) = f((x + 6)/2) = [2 / ((x + 6)/2)] - 6 ≠ x
So not inverses of each other.
Hence the correct option is A.
Learn more about Inverse functions here :
https://brainly.com/question/2541698
#SPJ7
lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies. She then had 3/7 of the container of sugar left. How much sugar was in the container at first
Answer:
At the beginning, there were 2,678.26 grams of sugar in the container.
Step-by-step explanation:
Since Lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies, and she then had 3/7 of the container of sugar left, to determine how much sugar was in the container at first, the following calculation must be performed:
880 + 1 / 10X = 3 / 7X
880 + 0.1X = 0.4285X
880 = 0.4285X - 0.1X
880 = 0.3285X
880 / 0.3285 = X
2,678.26 = X
Therefore, at the beginning there were 2,678.26 grams of sugar in the container.
Muhammad lives twice as far from the school as Hita. Together, the live a total of 12 km
from the school. How far away drom the school does each of them live?
Answer:
Muhammad lives 8 km away from the school.
Hita lives 4 km away from the school.
Step-by-step explanation:
First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.
Which theorem accurately completes Reason A?
hich theorem accurately completes Reason A
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000
Answer:
The correct answer is "76.98%".
Step-by-step explanation:
According to the question,
⇒ [tex]P(34000<x<46000) = P[\frac{34000-40000}{5000} <\frac{x- \mu}{\sigma} <\frac{46000-40000}{5000} ][/tex]
[tex]=P(-1.2<z<1.2)[/tex]
[tex]=P(z<1.2)-P(z<-1.2)[/tex]
[tex]=0.8849-0.1151[/tex]
[tex]=0.7698[/tex]
or,
[tex]=76.98[/tex]%
I need help with this
Samir estimates the value of Three-fifths times 16.1. Which estimate is reasonable?
3
9
12
15
Answer: 9
Step-by-step explanation:
[tex] \frac{3}{5} \times 16.1 = 9.66[/tex]
solve above question
if the volume of a cube is 2197cm3, find the height of the cube
To win the game, Elena has to roll an even number first and a number less than 3 second. Her probability of winning is StartFraction 6 over 36 EndFraction.
Answer:
Sum of 6
Sum of 2 or 9
Sum (> 2 but < 5)
Step-by-step explanation:
We are given that :
Elena's probability of winning is 6 /36 = 1/6
And also that Martha's probability if winning is lower Than that of Elena ; Hence, Martha's outcome should be outcjnes whose probability is less than 1/6 (Elena's probability of winning)
Using a sample space that gives the sum of 2 dices.
Recall :
Probability = required outcome / Total possible outcomes
Total possible outcomes for a two dice throw = 6² = 36
Using the sample space attached, we can count the sums from the sample space :
To obtain a sum of 7 :
P(sum 7) = 6 /36 = 1/6
To obtain a sum of 6 :
P(sum 6) = 5 /36
Sum of 2 or 9:
P(sum of 2 or 9). = 5 / 36
Sum > 9 :
P(sum > 9). = 6/36
P Sum (> 2 but < 5) = 5 /36
Correct choices are probability values less than 6/36 which are :
Sum of 6
Sum of 2 or 9
Sum (> 2 but < 5)
Answer:
rolling a sum of 6
rolling a sum of 2 or a sum of 9
rolling a sum that is greater than 2 but less than 5
Step-by-step explanation:
Find the area of the sector formed by central angle
θ
in a circle of radius
r
if
θ
=
2
;
r
=
6
m
Answer: 0.2pi
Step-by-step explanation:
1. Find the area of the entire circle
2. Set up a proportion that compares the relationship of the Area of sector and the Area of circle to the Arc measure and the circle measure
3. Solve!
Each minute Garret is able to run 124 meters. If he has already run 328 meters, what will his total distance be after 11 minutes?
A. 1,692 meters
B. 2,244 meters
C. 3,674 meters
D. 4,972 meters
Answer:
A.
Step-by-step explanation:
124 * 11 = 1364
1364 + 328 = 1,692
Serkan teacher regularly buys 75 TL of gasoline in his car every week.
At the end of the 13th week, how much is the total gasoline expenditure made by the serkan teacher?
A)390 B)420 C)900 D)975
Answer:
d
Step-by-step explanation:
75 per week,
after 13 weeks, 75*13 = 975
What is the range of possible sizes for side x? Please help!
Answer:
x is smaller than 5.6 and greater than 0
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
Rn(x) → 0.] Find the associated radius of convergence R.
f(x) = 8(1 − x)^−2
show step by step including finding the derivatives.
Recall that for |x| < 1, we have
[tex]\displaystyle \frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]
Differentiating both sides gives
[tex]\displaystyle \frac1{(1-x)^2} = \sum_{n=0}^\infty nx^{n-1} = \sum_{n=0}^\infty (n+1)x^n[/tex]
and multiplying both sides by 8 gives the series for f(x) :
[tex]f(x)=\displaystyle \frac8{(1-x)^2} = \boxed{8\sum_{n=0}^\infty (n+1)x^n}[/tex]
and this converges over the same interval, |x| < 1, so that the radius of convergence is 1.
two interior angles of a trapezium sum up to 250 degrees If the remaining angles are equal find the value
9514 1404 393
Answer:
each is 55°
Step-by-step explanation:
The sum of angles in a trapezium is 360°, so the sum of the remaining two angles is 360° -250° = 110°. Each of those two equal angles will be ...
110°/2 = 55°
The product of 86 and the depth of the river
Answer:
Step-by-step explanation:
Are you trying to find a variable expression? the product of 86 means multiplication so 86*n or 86n. Other than that I dont understand the question.
Find the probability of 3 success for the binomial experiment with 7 trial and the success probability of 0.3. Then find the mean and standard deviation. Write the formula substitute
the values.
Answer:
[tex]P(x=3)=0.2269[/tex]
Mean=2.1
Standard deviation=1.21
Step-by-step explanation:
We are given that
n=7
Probability of success, p=0.3
q=1-p=1-0.3=0.7
We have to find the probability of 3 success for the binomial experiment and find the mean and standard deviation.
Binomial distribution formula
[tex]P(X=x)=nC_xp^{x}q^{n-x}[/tex]
Using the formula
[tex]P(x=3)=7C_3(0.3)^3(0.7)^{7-3}[/tex]
[tex]P(x=3)=7C_3(0.3)^3(0.7)^{4}[/tex]
[tex]P(x=3)=\frac{7!}{3!4!}(0.3)^3(0.7)^{4}[/tex]
[tex]P(x=3)=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}(0.3)^{3}(0.7)^{4}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex]P(x=3)=0.2269[/tex]
Now,
Mean, [tex]\mu=np=7\times 0.3=2.1[/tex]
Standard deviation, [tex]\sigma=\sqrt{np(1-p)}[/tex]
Standard deviation, [tex]\sigma=\sqrt{7\times 0.3\times 0.7}[/tex]
Standard deviation, [tex]\sigma=1.21[/tex]
what is 24 subtracted from 8
Hi!
8 - 24 = -(24 - 8) = -16
Answer:
-16
Step-by-step explanation:
8-24=-16
b) What is the 4 times of the sum of 3and9?
Answer:
108
Step-by-step explanation:
sum is a fancy word for add so 3+9=27 and 27*4=108
Use the figure to find x.
Answer:
Step-by-step explanation:
The sides of a 30-60-90 triangle are in the ratio 1:√3:2
The side opposite the 30° angle is (12√6)÷2 = 6/√6.
The side opposite the 60° angle is √3×6/√6 = 6/√2 =3√2.
The sides of a 45-45-90 triangle are in the ratio 1:1:√2
The hypotenuse is 3√2, so the side opposite the 45° angle is 3.
x = 3
HELP!!!!
Which of the following is the absolute value of 6 − 3i?
A) 3i√3
B) 3√5
C) 3√5i
D) 3√3
Answer:
B
Step-by-step explanation:
We want to find the value of:
[tex]\displaystyle |6-3i|[/tex]
Recall that given a complex number z in the form:
[tex]z=a+bi[/tex]
The absolute value of z will be given by:
[tex]\displaystyle |z| = \sqrt{a^2+b^2}[/tex]
We have the complex number:
[tex]6-3i[/tex]
Thus, a = 6 and b = -3.
Then its absolute value will be:
[tex]|6-3i|=\sqrt{(6)^2+(-3)^2}[/tex]
Evaluate:
[tex]\displaystyle |6-3i|= \sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex]
Hence, our answer is B.
Given that fx=2x2-4x+1, then f(-1)is.
Answer:
[tex]f(-1)=7[/tex]
Step-by-step explanation:
I am going to assume your question meant the equation
[tex]f(x)=2x^{2} -4x+1[/tex]
So [tex]f(-1)[/tex] can be found by substituting all the x terms in the equation with -1
[tex]f(-1)=2(-1)^{2} -4(-1)+1[/tex]
And simplifying for our answer
[tex]f(-1)=2(1)+4+1[/tex]
[tex]f(-1) = 2+4+1[/tex]
[tex]f(-1)=7[/tex]
Please help …………………….
9514 1404 393
Answer:
(-3, 3)
Step-by-step explanation:
The blanks are trying to lead you through the process of finding the point of interest.
__
The horizontal distance from T to S is 9 . (or -9, if you prefer)
The ratio you're trying to divide the line into is the ratio that goes in this blank:
Multiply the horizontal distance by 2/3 . (9×2/3 = 6)
Move 6 units left from point T.
The vertical distance from T to S is 6 .
Multiply the vertical distance by 2/3 . (6×2/3 = 4)
Move 4 units up from point T.
__
Point T is (3, -1) so 6 left and 4 up is (3, -1) +(-6, 4) = (3-6, -1+4) = (-3, 3). The point that is 2/3 of the way from T to S is (-3, 3).
The following data points represent the number of remote controllers each student in Tria's video game club owns.
Sort the data from least to greatest.
0
0
7
7
4
4
2
2
0
0
1
1
8
8
0
0
10
2
2
5
5
Find the interquartile range (IQR) of the data set.
If u= 70% and o=5%, what % of scores fall within 3 standard deviations from the mean?
Answer:
"85%" is the right answer.
Step-by-step explanation:
Given:
[tex]\mu = 70[/tex] (%)
[tex]\sigma = 5[/tex] (%)
As we know,
The 99.7% observation fall within the 3rd standard deviation, then
⇒ [tex](\mu \pm \sigma ) = (70-(3\times 5)) \ to \ (70+(3\times 5))[/tex]
[tex]=(70-15) \ to \ (70+15)[/tex]
[tex]=55 \ to \ 85[/tex] (%)
Thus the above is the correct solution.