No,the population mean is not equal to 9.2 and the value in t statistic is -1.02.
Given sample size of 49,sample mean of 8.5,standard deviation of 1.5, significance level of 0.01.
We are required to find out whether the population mean is equal to 9.2 and the value of t in test statistic.
We have to first make the hypothesis for this.
[tex]H_{0}[/tex]:μ≠9.2
[tex]H_{1}[/tex]:μ=9.2
We have to use z statistic because the sample size is more than 30.
Z=(X-μ)/σ
We have been given sample mean but we require population mean in the formula so we will use sample mean.
Z=(8.5-9.2)/1.5
=-0.7/1.5
=-0.467
P value of -0.467 is 0.67975.
P value is greater than 0.01 so we will accept the hypothesis means population mean is not equal to 9.2.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
=(8.5-9.2)/1.5/[tex]\sqrt{49}[/tex]
=-0.7/0.21
=-1.02
Hence it is concluded that no,the population mean is not equal to 9.2 and the value in t statistic is -1.02.
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Barrett works at an ice cream shop. the function f(x) represents the amount of money in dollars barrett earns per gallon of ice cream, where x is the number of gallons of ice cream he makes. the function g(x) represents the number of gallons of ice cream barrett makes per hour, where x is the number of hours he works. f(x) = 2x2 4 g(x) = the square root of three times x cubed find f(g(x)). f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 dollars over hour f of g of x equals the square root of the quantity 6 times x to the fifth power plus 4 gallons over hour f(g(x)) = 6x3 4 gallons over hour f(g(x)) = 6x3 4 dollars over hour
Amount of money earned per number of hours of work = [tex]f(g(x)) = 6x^{3} + 4[/tex]
What is a composite function?A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.To evaluate a composite function f(g(x)) at some x = a, first compute g(a) by substituting x = a in the function g(x). Then substitute g(a) into the function f(x) by substituting x = g(a). In the same way, we can calculate g(f(a)) as well.
Required calculation -
Amount of money (the earning) per unit x = [tex]f(x) = 2x^{2} + 4[/tex]
Number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works = [tex]g(x) = \sqrt{3x^{3}}[/tex]
we are to find the composite function [tex]f(g(x))[/tex]
Substituting g(x) into the x of f(x), we find:
[tex]f(g(x)) = 2(\sqrt{3x^{3} } )^{2} + 4\\\\= 2(3x^{3} ) + 4\\= 6 x^{3} + 4[/tex]
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Answer:
f(g(x)) = 6x3 + 4 dollars over hour
Step-by-step explanation:
If g(x)=-2x), which graph is the graph of function g?
Answer:
The graph of g(x) has a y-intercept at (0,0) and a slope of -2.
Select the correct answer from each drop-down menu.
The number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9 Is
.The probability
that both the first digit and the last digit of the three-digit number are even numbers is
Reset
Next
Using it's concept, we have that the probability that both the first digit and the last digit of the three-digit number are even numbers is 2/27.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering that there are six numbers, out of which 4 are odd and 2 are even, we have that:
The first and last digits are even with 2/6 = 1/3 probability.The second digit is odd with 4/6 = 2/3 probability.Hence the desired probability is:
p = 1/3 x 2/3 x 1/3 = 2/27.
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20 points please help!!!!!
Answer:
a) Class A has the larger interquartile range.
b) Class A has the highest test score.
c) Class B has higher median test score.
d) Class B has smaller range of test score.
Step-by-step explanation:
a) Inter quartile range (IQR) = upper quartile - lower quartile
Class A: IQR = 79 - 65 = 14
Class B: IQR = 77 - 70 = 7
Class A has larger interquartile range.
b) Class A has the highest test score.
c) Median of class A = 70
Median of class B = 74
Class B has higher median test score.
d) Range is the difference between the highest and lowest score.
Range = highest score - lowest score
Range of Class A = 85 - 62 = 23
Range of class B = 79 - 68 = 11
Class B has smaller range of test score.
PLS HELP IM SUPER STUCK AAA
Answer:
(15,0) , (0,6)
Step-by-step explanation:
Same concept as the previous 2 questions.
x-intercept is where the line touches the x-axis, and y = 0.
when y = 0,
12x + 30(0) = 180
12x = 180
x = [tex]\frac{180}{12}[/tex]
x = 15
Therefore the coordinates of the x-intercept is (15,0)
y-intercept is where the line touches the y-axis, and x = 0.
when x = 0,
12(0) + 30y = 180
30y = 180
y = [tex]\frac{180}{30}[/tex]
y = 6
Therefore the coordinates of the y-intercept is (0,6)
Amal used the tabular method to show her work dividing –2x3 11x2 – 23x 20 by x2 – 3x 4.
The true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
How to determine the true statement?The complete question is added as an attachment
From the table, we have
Divisor = x^2 - 3x + 4
Quotient = 2x + 5
Dividend = -2x^3 + 11x^2 - 23x + 20
See that the signs of the leading coefficients of the dividend and the divisor are different
This means that the leading coefficient of the quotient must be negative
From the question, we have:
Quotient = 2x + 5
The expression 2x + 5 has a positive leading coefficient
Hence, the true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
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The area of rectangle is (a²+69+8) sq- units find the length
and breadth of the
rectangle
Step-by-step explanation:
Area of rectangle= length × breadth
A= a²+6a+8
= a²+4a+2a+8
= a(a+4) + 2(a+4)
= (a+4)(a+2)
length= a+4
breadth= a+2
please help! look at the photo linked
Answer:
3; 1
Step-by-step explanation:
when there are six spots we can see that there are 2 eyes
so
divide both sides by 2
6:2
6 / 2 : 2 / 2
3 : 1
that is your answer
Find the surface area of the composite figure.
5 cm
6 cm
20 cm
4 cm
5 cm 4 cm
SA =
12 cm
-6 cm
[?] cm²
Step-by-step explanation:
we have 2 blocks, as the graphic shows.
the surface areas of both blocks are the sum of their 6 sides each.
the special thing about seeing them as "composite figure" is that 2 sides (one for each block) are partly or even completely blocking each other off from being seen, so these parts and whole side are not part of the combined surface area.
let's start with the large block :
it is 5cm × 6cm × 20cm.
its surface area is the sum of
top and bottom 5×6
front and back 20×5
left 20×6
visible right (20 - 12)×6 = 8×6
it is (20-12)cm long, because the short block
is 12cm high.
so, we have
2 times 5×6 =2×30 = 60 cm²
2 times 20×5 = 2×100 = 200 cm²
20×6 = 120 cm²
8×6 = 48 cm²
in total : 428 cm²
now the small block :
it is 4cm × 6cm × 12cm.
its surface area is the sum of
top and bottom 4×6
front and back 4×12
no left (completely covered by the large block)
right 6×12
so, we have
2 times 4×6 = 2×24 = 48 cm²
2 times 4×12 = 2×48 = 96 cm²
6×12 = 72 cm²
in total : 216 cm²
the complete surface area of the composite figure is
428 + 216 = 644 cm²
Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function?
Answer:
Step-by-step explanation:
Equation
f(x) = (8x + 1) / (2x + 9)
Notice the brackets. They are necessary to show what comes before the division sign, and what comes after.
Behavior
The best way to state the behavior is to get something like a graphing program to show you what the curve looks like -- where it's critical points are for example. I use Desmos for this kind of question, Just do a search for Desmos and bookmark it. You will use it quite often.
So you want to know the behavior.
Right Curve
Crosses the x axis at (-0.125, 0)
Crosses the y axis at (0,0,111)
The right curve has a domain of -∞ < x < ∞
The right curve has a range of -∞ < x < ∞
The range is going to have to go out quite a ways before you see any dramatic decrease in the way it is drawn.
Left Curve.
The right hand curve never crosses either the x or y axis. Nor does it just touch the x or y axis.
The domain is -∞ <x < 0
The range is 0<x<∞
What is the approximate total volume of the silo? use 3.14 for π and round the answer to the nearest tenth of a cubic meter. 37.1 m3 71.9 m3 116.5 m3 130.8 m3
The total volume of silo is = 116.5[tex]{~m}^{3}[/tex]
The correct option is C
What are the geometric figures?Any arrangement of points, lines, or planes constitutes a geometric figure. Depending on their dimensions, geometric figures can be categorized as either a space figure, a plane figure, a line, a line segment, a ray, or a point.
Any object's surface area is the space that the object's surface takes up on a specific area or region. Volume, however, refers to how much room a thing has.
Given data:
Radius =4.4/2
=2.2
height of cylinder = 6.2
to find :
total volume of silo = volume of cylinder + volume of hemisphere
[tex]\begin{aligned}&=\pi r^{2} h+\frac{2}{3} \pi r^{3} \\&=\pi r^{2}\left(h+\frac{2}{3} r\right) \\&=\frac{22}{7} \times(2.2)^{2}\left[6.2+\frac{2 \times 2.2}{3}\right]\end{aligned}[/tex]
= 116.5[tex]m^2[/tex]
The total volume of silo is = 116.5[tex]m^2[/tex]
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I understand that the question you are looking for is:
A grain silo is composed of a cylinder and a What is the approximate total volume of the silo? Use hemisphere. The diameter is 4.4 meters. The height of 3.41 for [tex]\pi[/tex] and round the answer to the nearest tenth of its cylindrical portion is 6.2 meters. a cubic meter.
a. 37.1[tex]m^2[/tex]
b. 71.9 [tex]m^2[/tex]
c.116.5 [tex]m^2[/tex]
d. 130.8[tex]m^2[/tex]
The function f(x) = x2 6x 3 is transformed such that g(x) = f(x − 2). find the vertex of g(x).
the vertex of the function g(x) = f(x 2) .
A quadratic equation's vertex form is defined.If a quadratic equation is expressed as the following
[tex]y=a(x-h)^{2}+k[/tex]
It is then said to be in vertex form. Because the vertex point (peak point) occurs on the graph of this equation, it is so named (h,k)
The parabola that the quadratic equation depicts has this point (h,k) as its vertex.
How may the given equation be changed to be in vertex form?We first remove the x squared coefficient, and then inside the bracket, we strive to create a condition that resembles a perfect square.
So, this is what we have:
[tex]$f(x)=x^{2}+6 x+3$\\$g(x)=f(x-2)$[/tex]
Thus, we obtain:
[tex]\begin{aligned}&g(x)=f(x-2) \\&g(x)=(x-2)^{2}+6(x-2)+3 \\&g(x)=x^{2}-4 x+4+6 x-12+3 \\&g(x)=x^{2}+2 x-5\end{aligned}[/tex]
Vertex form transformation of g(x):
[tex]\begin{aligned}&g(x)=x^{2}+2 x-5 \\&g(x)=x^{2}+2 x+1-1-5 \\&g(x)=(x+1)^{2}-9 \\&g(x)=(x-(-1))^{2}-6 \\&g(x)=(x-(-1))^{2}+(-6)\end{aligned}[/tex]
By comparing this[tex]a(x-h)^{2}+k[/tex] to, we obtain the coordinates of the vertex of the graph of g(x) as (h,k) = (-1,-6), as shown below.
As a result, the vertex of the function g(x) = f(x 2) .
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Given the functions k(x) = 2x2 − 5 and p(x) = x − 3, find (k ∘ p)(x). (k ∘ p)(x) = 2x2 − 6x 4 (k ∘ p)(x) = 2x2 − 12x 13 (k ∘ p)(x) = 2x2 − 12x 18 (k ∘ p)(x) = 2x2 − 8
[tex](k \circ p)(x)=k(p(x))=k(x-3) \\ \\ =2(x-3)^2-5 \\ \\ =2(x^2 - 6x+9)-5 \\ \\ =\boxed{2x^2 - 12x+13}[/tex]
For instance, f[g (x)] exists the composite function of f(x) and g(x). The composite function f[g (x)] exists read as “f of g of x”.
The composite function exists [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex]
Therefore, the correct answer is option b. [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex].
What is the composite of a function?A composite function exists generally as a function that exists written inside another function. The composition of a function exists done by replacing one function with another function.
Given function exists, [tex]$k(x)=2 x^{2}-5[/tex] and p(x) = (x - 3)
To find composite function k(p(x)).
k(p(x)) = k(x-3)
[tex]$&k(p(x))=2(x-3)^{2}-5 \\[/tex]
simplifying the above equation, we get
[tex]$&k(p(x))=2\left(x^{2}+9-6 x\right)-5 \\[/tex]
[tex]$&k(p(x))=2 x^{2}+18-12 x-5 \\[/tex]
[tex]$&k(p(x))=2 x^{2}-12 x+13[/tex]
The composite function exists [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex]
Therefore, the correct answer is option b. [tex]$k(p(x))=2 x^{2}-12 x+13$[/tex].
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Find the polar equation of an ellipse with its focus at the pole and vertices at (−1,0) and (3,0).
The polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
The vertices of ellipse are (−1,0) and (3,0).
The polar equation of an ellipse can be represented as
[tex]r=\frac{ep}{1+ecos\theta}[/tex]
where e is the eccentricity.
Eccentricity, e = [tex]\frac{c}{a}[/tex]
c is the distance from the center to the focus and a is the distance from the center to the vertex
[tex]c=\frac{3-(-1)}{2}[/tex]
⇒ [tex]c=\frac{4}{2}[/tex]
⇒ c = 2
[tex]a=\frac{3+(-1)}{2}[/tex]
⇒ [tex]a=\frac{2}{2}[/tex]
⇒ a = 1
Then, e = [tex]\frac{2}{1}[/tex]
⇒ e = 2
Now, the polar equation of an ellipse becomes as,
⇒ [tex]r=\frac{2p}{1+2cos\theta}[/tex] ------- (1)
Now plug in a vertex point such as (-1,0) and solve for p,
⇒ [tex]-1=\frac{2p}{1+2cos0}[/tex]
⇒ [tex]-1=\frac{2p}{1+2(1)}[/tex] [∵ cos 0 = 1]
⇒ [tex]-1=\frac{2p}{3}[/tex]
⇒ [tex]-3=2p[/tex]
⇒ [tex]p=-\frac{3}{2}[/tex]
Thus the polar equation of an ellipse (1) becomes as,
⇒ [tex]r=\frac{2(-\frac{3}{2} )}{1+2cos\theta}[/tex]
⇒ [tex]r=-\frac{3}{1+2cos\theta}[/tex]
Hence we can conclude that the polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
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Using the graph of the function g(x) = log3 (x – 4), what are the x-intercept and asymptote of g(x)?
The x-intercept is when y=0, but since [tex]\log_{3}(x-4) \neq 0 \text{ } \forall x[/tex], there is no x-intercept.
The asymptote is when the argument equals 0, which is at x=4.
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes.
Let x represent the number of quick washes and let y represent the number of premium washes. Which system of linear equations represents the situation?
The system of linear equations represents the situation is;
x + y = 125
x + y = 1255x + 8y = 775
Simultaneous equationSimultaneous equation is an equation in two unknown values are being solved for at the same time.
let
number of quick washes = xnumber of premium washes = yx + y = 125
5x + 8y = 775
From equation (1)
x = 125 - y
5x + 8y = 775
5(125 - y) + 8y = 775
625 - 5y + 8y = 775
- 5y + 8y = 775 - 625
3y = 150
y = 150/3
y = 50
Substitute y = 50 intox + y = 125
x + 50 = 125
x = 125 - 50
x = 75
Therefore, the number of quick washes and premium washes Monica’s school band had is 75 and 50 respectively.
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Answer:
A. 5x + 8y = 775 and x + y =125
Step-by-step explanation:
The ratio is: 450g to 1kg
In it's simplest form
Answer:
9:20
Step-by-step explanation:
1kg is 1000g grams and in order to simify we need the units to be equal . 450:1000 would simplify to
45: 100 by divinding both the number by 10 then divide both number by 5 which would give 9: 20
hopefully this helped . if you need any more explanation pls ask
pls give brainliest if you like my answer :) thanks
Answer:
9: 20
Step-by-step explanation:
First, we have to convert both figures into the same unit.Here we can convert both into grams.As 450g is already given in grams, let us convert 1kg into grams.To convert kilograms into grams we have to multiply kilograms by 1000.Therefore,1kg × 1000 = 1000g
Now let us write those as a ratio.450 : 1000g
450 : 1000
To write the ratio in the simplest form we can divide both by 50.9: 20
As this cannot be simplified anymore, the simplest form of 450: 1000 is 9: 20.write the expression as the sine or cosine of an angle
The expression, written as the sine of an angle is sin (7π/10)
Trigonometry IdentitiesFrom the question, we are to write the given expression as the sine or cosine of an angle.
The given expression is
sin(π/5)cos(π/2) + sin(π/2)cos(π/5)
Let A = π/5
and
B = π/2
Thus, we get
sinA cosB + sinB cosA
From the given information, we have that
sin(A ± B) = sinA cos B ± cosA sinB
∴ sin(A + B) = sinA cos B + cosA sinB
Now,
sinA cosB + sinB cosA = sinA cosB + cosA sin B
∴ sinA cosB + sinB cosA = sin (A + B)
Put A = π/5
and
B = π/2
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)
Hence, the expression, written as the sine of an angle is sin (7π/10)
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radians and degrees
180° irc =
[tex]\Large\texttt{Answer}[/tex]
[tex]180^\circ=\pi\:radians}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ For converting from degrees to radians, use this conversion factor:
[tex]\bf{\cfrac{\pi}{180}}[/tex]
⇨ Convert
[tex]\bf{\cfrac{180}{1}\times\cfrac{\pi}{180}}[/tex]
⇨ The 180s cancel out, and we have:
[tex]\pi[/tex]
Hence
[tex]\bf{180^\circ=\pi\:radians}[/tex]
Hope that helped
use the compound interest formulas A=P e^rt to solve the problem given. round answers to the nearest cent.
Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 5.5% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Answer:
a) $20,771.76
b) $20,817.67
c) $20,484.80
d) $20,864.52
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedPart (a): semiannually
Given:
P = $15,000r = 5.5% = 0.055n = 2t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{2}\right)^{2 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1.0275}{2}\right)^{12}[/tex]
[tex]\implies \sf A=20771.76[/tex]
Part (b): quarterly
Given:
P = $15,000r = 5.5% = 0.055n = 4t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{4}\right)^{4 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1.01375}\right)^{24}[/tex]
[tex]\implies \sf A=20817.67[/tex]
Part (c): monthly
Given:
P = $15,000r = 5.5% = 0.055n = 12t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{12 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{72}[/tex]
[tex]\implies \sf A=20484.80[/tex]
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Part (d): continuous
Given:
P = $15,000r = 5.5% = 0.055t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000e^{0.055 \times 6}[/tex]
[tex]\implies \sf A=20864.52[/tex]
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A line passes through the point (7, 3. and has a slope of 2. Write an equation for this line.
Answer:
y = 2x - 11.
Step-by-step explanation:
Use the point-slope form of the straight line.
y - y1 = m(x - x1) where m = slope and (x1, y1) is the given point.
Here m = 2 and (x1, y1) = (7,3) so the equation is:
y - 3 = 2(x - 7)
y - 3 = 2x - 14
y = 2x - 11
Given the linear regression equation, y^=134. 63−2. 79x. What is the predicted value of y^ when x=45? (round answer to two decimal places, example: 3. 45)
Answer:
9.08
Step-by-step explanation:
To find the predicted value of y, put the x-value where x is in the equation and do the arithmetic.
Substitution[tex]\hat{y}=134.63-2.79x\qquad\text{given}\\\\\hat{y}=134.63-2.79(45) = 134.63-125.55\qquad\text{use 45 for x}\\\\\boxed{\hat{y}=9.08}\qquad\text{simplify}[/tex]
Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
Prove: △HKJ ~ △LNP
Triangles H K J and L N P are shown. Triangle L N P is smaller and to the right of triangle H K J.
Statement Reason
1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. given
2. m∠H + m∠J + m∠K = 180° 2. ?
3. 30° + 50° + m∠K = 180° 3. substitution property
4. 80° + m∠K = 180° 4. addition
5. m∠K = 100° 5. subtraction property of equality
6. m∠J = m∠P; m∠K = m∠N 6. substitution
7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent
8. △HKJ ~ △LNP 8. AA similarity theorem
Which reason is missing in step 2?
CPCTC
definition of supplementary angles
triangle parts relationship theorem
triangle angle sum theorem
Answer:
triangle angle sum theorem
Step-by-step explanation:
The missing statement is one that justifies the sum of the angles in a triangle being 180°.
That justification is provided by the ...
triangle angle sum theorem
The Data
Decorative glass pebbles are often used in vases for their appearance, and to have their weight stabilize the vase. The table below gives the total weight of a vase full of uniform glass pebbles.
TABLE OF DATA ATTACHED BELOW*
The Analysis
1- Using the table of data above, determine if this relationship is linear or not. Explain how you know.
2-Write an equation that best represents this relationship:
Explain how you reach your answer and show your work below.
3- Graph the data on the grid to the right, label both axes, and label it Line 1.
4-
a) What is the meaning of the initial value in this scenario?
b) What is the meaning of the slope in this scenario?
5- How would the graph AND equation change if a Styrofoam cup is used to collect the data, instead of a glass vase? Explain your reasoning.
6- Based on your equation in question #2, how much will 112 pebbles weigh with the vase?
7- If the total weight is 504 g, how many pebbles are in the vase?
8- Your friend Wilma shares her analysis of similar data about pebbles and a vase, but her equation is W = 10p + 80.
a) Graph it on the same grid as question #3. Label it Line 2.
b)What are the coordinates of the point of intersection?
c)What does it mean in this scenario?
9- Write a SIMPLIFIED algebraic expression to represent the area of the following trapezoid. Show all your work.
(Hint: area of a trapezoid = [tex]\frac{h(a+b)}{2}[/tex])
TRAPEZOID ATTACHED BELOW*
10- Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah. What is the age of Tanya and Leah now?
I NEED IT TODAY PLESE!
With the aid of the attached diagrams in the question, we have;
1- Linear relation
2- W = 8•P + 80
3- Please find attached the graph created using a graphing calculator.
4- a) The initial value is the mass of the vase
b) The slope is the mass of each pebble
5- The initial value is lesser than 80
6- 1.2 kilograms
7- 53 pebbles
8- a)
b) (0, 80)
c) The masses are the same
9- Trapezoid area, A = 14•x² - 4•x
10- Tanya and Leah are 18 and 6 years old respectively
How can the table and diagram be analyzed?1- The relationship between two variables (x and y) is linear if the difference between the terms of the x-values and the terms of the y-values are both constant.
From the table we have;
The difference between consecutive terms of the x-values is constant and equal to 10The difference between consecutive terms of the y-values is constant and equal to 80The relationship between the x and y-values in the table is therefore;
A linear relationship2. The slope, m, of the linear function is found as follows;
m = (360 - 280)/(30 - 20) = 8
The equation is therefore;
W - 360 = 8•(P - 30)
W = 8•P - 240 + 360 = 8•P + 80
The equation is; W = 8•P + 803. Please find attached the graph drawn with a graphing calculator.
4. The initial value is the output variable (W-value) when the input variable (P-value) is zero.
Therefore;
y = 8×0 + 80 = 80
a) The initial value indicates when the input, P-value is zero, which gives the mass of the vases
b) The slope indicates the number of times an additional pebble increases the weight of the vase and pebble, which is the mass of one pebble
5- A styrofoam cup is lighter than a glass cup, therefore, the initial value, which is the constant term, c, reduces.
The change is that, the initial value reduces and becomes less than 806- The weight, W, of 112 pebbles is therefore;
W = 10 × 112 + 80 = 1,200
The weight of 112 pebbles is 1,200 g, which is 1.2 kg.7- 504 = 8•P + 80
Which gives;
504 - 80 = 8•P
P = 424 ÷ 8 = 53
The number of pebbles in the vase when it weighs 504 g. is 53 pebbles8- Wilma's equation is; W = 10•P + 80
a) Please find the second graph showing the graphs of the two equations combined.
b) The point of intersection is given by the relation 10•P + 80 = 8•P + 80
2•P = 0
P = 0
Therefore, at the point of intersection, W = 80
The coordinates of the point of intersection is therefore;
(0, 80)c) The point of intersection means that the weight of Wilma's vase and the vase in question 1 are the same.
9. The area of the trapezoid, A, can be expressed as follows;
A = 4•x × ((2•x + 5)+(5•x - 7))/2
A = 2•x × (7•x - 2) = 14•x² - 4•x
Area of the trapezoid = 14•x² - 4•x10. Let T represent Tanya's age now and let L represent Leah's current age, we have;
T = L + 12
T - 3 = (L - 3) × 5
Solving gives;
L + 12 - 3 = (L - 3) × 5 (Substitution property)
L + 9 = 5•L - 15
4•L = 9 + 15 = 24
L = 24 ÷ 4 = 6
Leah's age now, L = 6 yearsT = L + 12
Therefore;
T = 6 + 12 = 18
Tanya's age now, T = 18 yearsLearn more about writing equations here:
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2. A football team plays 28 games and wins 4 out of every 7 games played. No match ended in a draw. 20 (a) How many times has this football team lost?
PLS HELP IM STUCK PLS
Answer:
-4
Step-by-step explanation:
We are going to substitute 0 in for x and solve for y.
-2(0)+ 8y = -32 Anything times zero is zero
0 + 8 y = -32 Anything plus zero is itself.
8y = -32 Divide both sides by 8
y = -4
Evaluate the expression for f = -6 and g = -1.
fg - f =
Answer:
7
Step-by-step explanation:
Given the information from the question:
[tex]fg - f = f \times g - f[/tex]
Next we can use the order of operations to find the value of the expression.
[tex]fg - f = - 6 \times - 1 - ( - 1) \\ = 6 - ( - 1) \\ = 6 + 1 \\ = 7[/tex]
PLS HELP ASAP! Ty
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
The function can be solved as follows:
(h - g)(2.1) = 3.51
How to solve a function?g(x) = 2x² + 3x - 9
h(x) = x² + 2x - 6
(h - g)(x) = h(x) - g(x)
(h - g)(x) = 2x² + 3x - 9 - ( x² + 2x - 6)
(h - g)(x) = 2x² + 3x - 9 - x² - 2x + 6
(h - g)(x) = 2x² - x² + 3x - 2x - 9 + 6
(h - g)(x) = x² + x - 3
Therefore,
(h - g)(2.1) = (2.1)² + (2.1) - 3
(h - g)(2.1) = 4.41 + 2.1 - 3
(h - g)(2.1) = 6.51 - 3
(h - g)(2.1) = 3.51
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to set up a model linear equation to fit real world applications, what should always be the first step?
Answer:
Define the variables.
Step-by-step explanation:
Define the variables, then set up the equations, and finally solve the system using graphing, substitution, or elimination method.
To set up or model a linear equation to fit a real-world application, First, we have to determine the known amounts or quantities before defining the unknown quantity as a variable.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
To set up a model linear equation to fit real-world applications
In the first step determine known amounts or quantities.
Then, assign the unknown amount to a variable.
Now, find a method or approach to express the second unknown in terms of the first if there are many unknown quantities.
Create an equation that translates the words into mathematical functions.
Complete the equation. Make certain that the solution, including the system of measurement, can be expressed in words.
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Please help!! due in 2 hours!!
Answer:
i think 80 copies
Step-by-step explanation:
