PLEASE HELP!!!!!!!!!!!!!
Tasha used the pattern in the table to find the value of 4 to the power of -4
(refer to the graph)
She used these steps.
(refer to the picture of the steps)
In which step did Tasha make the first error?
Step 1
Step 2
Step 3
Step 4
Answers
Answer:
Tasha made her mistake in step 4.
Answer:
Step 4 is the incorrect.
Step-by-step explanation:
From the table attached,
Step 1. Find a pattern in the table.
Correct
Step 2. Find the value of [tex]4^{-3}=(\frac{1}{16})(\frac{1}{4})=\frac{1}{64}[/tex]
Correct
Step 3. Find the value of [tex]4^{-4}=(\frac{1}{64})(\frac{1}{4})=\frac{1}{256}[/tex]
Correct
Step 4. Rewrite the value of [tex]4^{-4}[/tex]
[tex](\frac{1}{256})=-\frac{1}{4^{-4} }[/tex]
Incorrect.
Because it should be [tex](\frac{1}{256})(\frac{1}{4})=\frac{1}{1024}[/tex]
Related Questions
Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase. Which models can be used to solve the problem? ; ; ; ;
Answers
Answer:
0.60b + 0.30w = 150; 60 + 0.30w = 150
Step-by-step explanation:
Answer:
C. 0.60b + 0.30w = 150; 60 + 0.30w = 150
Step-by-step explanation:
One zero of the polynomial function f(x) = x3 + x2 + 20x is x = 0. What are the zeros of the polynomial function?
0, −5, −4
0, −5, 4
0, 5, −4
0, 5, 4
Answers
The zeros of the polynomial function f(x) = x^3 + x^2 + 20x are 0, -5, -4.
Explanation:The zeros of a polynomial function are the values of x that make the function equal to zero.
We are given that one zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0.
To find the other zeros, we can use polynomial long division or synthetic division to factor out x = 0 and find the remaining quadratic equation.
Factoring the quadratic equation, we find that the zeros are x = -5 and x = -4.
Therefore, the correct answer is 0, -5, -4.
Final answer:
The zeros of the polynomial function f(x) = x^3 + x^2 + 20x are 0, -5, and -4.
Explanation:
The zeros of a polynomial function are the values of x that make the function equal to zero. Given that one zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0, we need to find the other zeros. To do this, we factor the polynomial using synthetic division or long division. In this case, the factored form of the polynomial is f(x) = (x)(x + 5)(x + 4). Therefore, the zeros of the polynomial function are 0, -5, and -4.
Wave Corporation began the current year with a retained earnings balance of $25,000. During the year, the company corrected an error made in the prior year, which was a failure to record depreciation expense of $5,000 on equipment. Also, during the current year, the company earned net income of $15,000 and declared cash dividends of $5,000. Compute the year-end retained earnings balance.
Answers
Answer:
$30,000.
Step-by-step explanation:
Wave Corporation began the current year with a retained earnings balance of $25,000.
Depreciation expense was of $5000
During the current year, the company earned net income of $15,000
Also gave cash dividends of $5,000.
So, year end retained earnings will be :
Year end retained balance = total net income minus net losses and dividends.
[tex]25000-5000+15000-5000=30000[/tex] dollars
The answer is $30,000.
What is the equation of the midline for the function f (x)?
f (t) = 3 cos (x) – 2.5
Answers
Answer:
y = -2.5
Step-by-step explanation:
For such a problem as this, you can replace all sine or cosine functions with their midline value of 0. Then you have ...
f(x) = 0 -2.5
which simplifies to ...
f(x) = -2.5
You can leave the equation like this, or write it as ...
y = -2.5
_____
Perhaps you can see that the midline is the value of any constant added to a sine or cosine function.
Answer: y=-2.5
Step-by-step explanation:
Suppose you just received a shipment of six televisions. Three of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Answers
Answer:
.6094
Step-by-step explanation:
Ten of 16 students in Nyack's class are girls. His teacher selected two helpers by randomly drawing names. He drew a boys name first and then a girls names. Nyack thinks that the probability of this happening is 15/64. Is he correct? If not, Explain his error.
Answers
[tex]|\Omega|=16\cdot15=240\\|A|=6\cdot10=60\\\\P(A)=\dfrac{60}{240}=\dfrac{1}{4}[/tex]
He's wrong.
If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, what is the height of the cup? Use 3.14 to for pi. Round your answer to the nearest hundredth. 6.76 inches 18.56 inches 21.97 inches 23.00 inches
Answers
Answer:
21.97 in
Step-by-step explanation:
Use the formula for the volume of a cone, fill in the given information, and solve for the height.
V = (1/3)πr²h
23 in³ = (1/3)(3.14)(1 in)²h . . . . . . . . with given numbers
3·23 in³/(3.14 in²) = h ≈ 21.97 in . . . . . divide by the coefficient of h
Answer:
21.97 inches
Step-by-step explanation:
If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, the height of the cup is 21.97 inches.
Round your answer to the nearest hundredth.
PLEASE HELP ASAP!!
At a frozen yogurt store, customers can purchase gelatin spheres as a yogurt topping. Each sphere contains 100.48/3 cubic millimeters of gelatin. Which statements about the measurements of the sphere are true? Check all that apply. (Use 3.14 for π. Recall that the formula for the volume for a sphere is V= 4/3πr³ .)
The radius of a sphere is 8 millimeters.
The radius of a sphere is 2 millimeters.
The circumference of the great circle of a sphere is 9.42 square millimeters.
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 square millimeters.
The surface area of a sphere is 25.12 square millimeters.
Answers
Answer:
The radius of a sphere is 2 millimeters
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 millimeters.
Step-by-step explanation:
Verify each statement
case A) The radius of a sphere is 8 millimeters
The statement is false
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=100.48/3\ mm^{3}[/tex]
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]100.48/3=\frac{4}{3}(3.14)r^{3}[/tex]
[tex]r^{3}=(100.48)/(4*3.14)[/tex]
[tex]r=2\ mm[/tex]
case B) The radius of a sphere is 2 millimeters
The statement is True
(see the case A)
case C) The circumference of the great circle of a sphere is 9.42 square millimeters
The statement is false
The units of the circumference is millimeters not square millimeters
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]C=2(3.14)(2)[/tex]
[tex]C=12.56\ mm[/tex]
case D) The surface area of a sphere is 50.24 square millimeters.
The statement is True
Because
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]SA=4(3.14)(2)^{2}[/tex]
[tex]SA=50.24\ mm^{2}[/tex]
case E) The circumference of the great circle of a sphere is 12.56 millimeters.
The statement is true
see the case C
case F) The surface area of a sphere is 25.12 square millimeters
The statement is false
because the surface area of the sphere is [tex]SA=50.24\ mm^{2}[/tex]
see the case D
Answer:
B, D,E
Step-by-step explanation:
Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent 555 minutes in total giving both instructions, and spoke 270 more words in Polish than in Hungarian. How long did Sakura speak in Hungarian, and how long did she speak in Polish?
Answers
Answer:3 minute
Step-by-step explanation:
Sakura speaks hungarian =150 words per minute
Sakura speaks polish =190 words per minute
and it is given she speaks 270 more words in polish than in hungarian
She speaks for a total of 5 minutes
let she speaks hungarian for t mins
therefore [tex]150\times t+270=190\left ( 5-t\right )[/tex]
t=2 mins
therefore sakura speaks hungarian for 2 mins and polish for 3 mins
Sakura speaks hungarian for 2 mins and polish for 3 mins
Matilda sits on her back porch for one hour every morning for a week and record the types and numbers of birds that viste her bird feeder what kind of study is this ?
Answers
Observational study.
------APEX
Answer:
d.Step-by-step explanation:
The choices for this question are
a. Double-blind study
b. Experiment
c. Sample survey
d. Observational study
The right answer would be d. Observational study, because this type of study is defined as an empirical and non-experimental research where all information is obtained by observation. When we apply this study, we try to find a cause-effect relation by observing the phenomenon as it naturally happens, that is, without interfering with the course of events like experimental investigations do.
So, in this case, Matilda is just observing, without altering anything that could influence the birds. She just sits observe and recover information, that's an observational study.
Therefore, the right answer is d.
Please help on these questions about Slopes on Graphs !!!!
Answers
Answer:
a) {C, D}, {B, E}, A . . . . four possible equivalent answers (explanation below)
b) Line C shows a "directly proportional" relationship
Step-by-step explanation:
Slope is the ratio of "rise" (vertical change) to "run" (horizontal change). Positive changes are "up" and "right".
Line A -- has no vertical change, so its slope is 0.
Line B -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4.
Line C -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2.
Line D -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2. This is the same slope as line C, so neither is greater than the other.
Line E -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4. This is the same slope as line B, so neither is greater than the other.
If we use alphabetical order to rank equal slopes, then the slopes (greatest to least) are ...
C (1/2), D (1/2), B (1/4), E (1/4), A (0)
_____
A "directly proportional" relationship graphs as a straight line through the origin. The only line passing through the point where the x- and y-axes meet is line C.
Line C represents a proportional function.
A curve passes through the point ????0, 5???? and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
Answers
Answer:[tex]y=2x^2[/tex]
Step-by-step explanation:
Given Curve passes through [tex]\left ( 0,5\right )[/tex]
Also the slope of the curve at every point p is twice the Y-coordinate of p
Let the coordinate of p be[tex] \left ( x,y\right )[/tex]
Therefore
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=2y[/tex]
[tex]\frac{dy}{y}=2dx[/tex]
Integrating both sides
[tex]\int \frac{dy}{y}=\int 2dx[/tex]
[tex]\ln y=2x+c[/tex]
Substituting values
[tex]\ln 5=c[/tex]
[tex]\ln \frac{y}{5}=2x[/tex]
[tex]y=2x^2[/tex]
Its in the picture below
a: 1% decay
b: 10% decay
c: 9% growth
d: 90% growth
Answers
Answer:
b: 10% decay
Step-by-step explanation:
Expressed as a percentage change, the growth is usually the value of the base of the exponential function after 1 has been subtracted. That result is expressed as a percent:
0.9 - 1 = -0.10 = -10% . . . . . 10% decay
_____
The "t/12" exponent means this is the decay that is experienced over 12 units of time. This might be the annual decay, where t is expressed in months, for example.
What would be the steps for finding the equation for the function f(x) based on the graph (the blue line) and what would the equation be? Please include steps that are universal to finding the equation of any possible graphed function, as I really don't even know where to begin and would like to be able to solve problems like this on my own one day. Thanks! :)
Answers
Answer:
f(x) = -2|x-2| +4
Step-by-step explanation:
Step 1: recognize this as an inverted, scaled, and translated absolute value function.
Step 2: identify the scale factor as 2, because each section has a "rise" of 2 for each "run" of 1. The scale factor is -2 because the function is inverted (reflected across the x-axis).
Step 3: identify the vertex* as (2, 4).
Step 4: Use the scale factor and translation information to make the transformation ... (let abs(x) represent the absolute value function)
f(x) = (scale factor)×abs(x -horizontal shift) + (vertical shift)
f(x) = -2|x -2| +4
_____
* The vertex is an identifiable point on the graph of this function. Knowing how the vertex is translated tells you how the whole function is translated. In general, you want to use an identifiable point (a turning point, point of symmetry, extreme point, whatever) when you're trying to determine the translation. For some functions, like a line, there is no specific identifiable point, so determining any specific translation is difficult or impossible.
_____
Comment on writing functions from graphs
One of the reasons for studying different functions is so you can learn to recognize their shape, and associate a formula and certain properties with that shape.
_____
The attached graph shows the parent absolute value function in blue and the transformed function f(x) in red.
I’m confused. Please help?
Answers
Step-by-step explanation:
[tex] f(x) = \log_a x [/tex]
[tex] \dfrac{f(x + h) - f(x)}{h} = [/tex]
[tex] = \dfrac{log_a(x + h) - \log_a x}{h} [/tex]
[tex] = \dfrac{log_a \dfrac{x + h}{x}}{h} [/tex]
[tex] = \dfrac{1}{h}log_a ( 1 + \dfrac{h}{x} ) [/tex]
[tex] = log_a ( 1 + \dfrac{h}{x} )^{\frac{1}{h}} [/tex]
Simplify the following? (x^4y)^3
Answers
Answer:
(x^12y)
Step-by-step explanation:
= (x^4y)^3
= (x^12y)
Answer:
The simplified form of given expression is x¹²y³
Step-by-step explanation:
Points to remember
Identities
(xᵃ)ᵇ = xᵃᵇ
xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
To find the simplified form
It is given that, (x⁴y)³
By using the above identities we can write (x⁴y)³ as,
(x⁴y)³ = (x⁽⁴ * ³ ⁾ * y³
= x¹² * y³
= x¹²y³
Therefore the simplified form of given expression is x¹²y³
Geometry:
The vertices of triangle ABC are A(0,9), B(-9,-9), C(9,-9) Find the scale factor if the image of ABC has vertices A'(3,10),B'(-1,2),C'(7,2)
Answers
Answer:
4/9
Step-by-step explanation:
The easiest segment to work with is BC, since the y-values are the same for coordinates B and C and for B' and C'.
The length of BC = 9 -(-9) = 18.
The length of B'C' = 7 -(-1) = 8.
The scale factor is B'C'/BC = 8/18 = 4/9.
Please help show that the following are TRUE.
Answers
Answer:
see below
Step-by-step explanation:
The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...
sum = a1/(1 -r)
Applying this to the given series, we get ...
a. sum = 5/(1 -3/4) = 5/(1/4) = 20
b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)
_____
The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...
S -rS = a1
S = a1/(1 -r)
Consider the system of linear equations. 5x+10y=15 10x+3y=13 To use the linear combination method and addition to eliminate the x-terms, by which number should the first equation be multiplied?
A- -2
B- -1/2
C- 1/2
D- 2
Answers
Answer:
A: -2
Step-by-step explanation:
You want some factor k such that k(5x) +(10x) = 0. That is, 5k+10 = 0. The solution to this is k=-2, corresponding to selection A.
k = -2 for sure
I normally multiply 5x+10y=15 by -2 to cancel out the x's.
This is because you can only solve the problem if one of your variables is canceled out and then you solve!
Danny is installing a fence around his rectangular yard. His yard is 20 feet long by 45 feet wide. If the fencing he picked out costs 25$ per foot, how much money will Danny spend on the fence?
Answers
Find the perimeter of the yard ( the distance around the yard).
A rectangle has two sides of each dimension.
The perimeter is 20 + 20 + 45 + 45 = 130 feet.
Now multiply the total feet by the cost per foot:
130 feet x 25 per foot = $3,250 total.
Danny needs to spend on his yard $3250 to fencing.
What is a rectangle?The rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Length of fence = Perimeter of his yard(rectangle)
Perimeter of rectangle = 2( length + width).
Perimeter of fence =2 ( 20 + 45 )
The perimeter of fence =130 foot.
Now
Cost = $25 per foot
So,
Cost of 130 feet at the rate of $25 per foot
⇒ 130 × 25 = $3250
Hence, Danny needs to spend on his yard $3250 to fencing.
For more about rectangles,
https://brainly.com/question/15019502
#SPJ2
A man steps out of a plane at a height of 4,000m above the ground falls 2,000m very quickly and then opens his parachute and slowly falls the remaining 2000m to the ground what height above the ground would be the best Choice for a reference point
Answers
Answer:
Step-by-step explanation:
A man steps out of a plane at 4,000m of height above the ground.The point at which he jumps out of the plane would make a good reference point. However, if his acceleration is going to change as a result of him opening his parachute 2000m above the ground, a good reference point would be there. Keep in mind though, that his velocity at that instant would need to be known for it to be useful- otherwise the airplane reference point would be just as good with appropriate modeling....
Answer:4000m easy !!
A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance.
Answers
Answer:
the music is both dubstep and trance
Six pairs of data yield r = 0.444 and the regression equation y = 5x + 2. also, y = 18.3. what is the best predicted value of y for x = 5?
Answers
The best predicted value of y for x = 5 is 27.
Explanation:A regression equation is a mathematical model that represents the relationship between a dependent variable and one or more independent variables. It expresses the linear or nonlinear association between these variables and is derived from statistical methods like linear regression analysis.
To predict the value of y for x = 5 using the regression equation, you can substitute x = 5 into the equation y = 5x + 2:
y = 5(5) + 2 = 27
Therefore, the predicted value of y for x = 5 is 27.
The best predicted value of [tex]\( y \) for \( x = 5 \) is \( y = 27 \).[/tex]
To find the best predicted value of [tex]\( y \) for \( x = 5 \),[/tex]we substitute [tex]\( x = 5 \)[/tex] into the regression equation:
[tex]\[ y = 5x + 2 \] \[ y = 5(5) + 2 \] \[ y = 25 + 2 \] \[ y = 27 \][/tex]
To reconcile this discrepancy, if we assume that the provided value of [tex]\( y = 18.3 \)[/tex] corresponds to [tex]\( x = 5 \),[/tex] then we would set the regression equation equal to 18.3 and solve for \( x \):
[tex]\[ 18.3 = 5x + 2 \] \[ 16.3 = 5x \] \[ x = \frac{16.3}{5} \] \[ x = 3.26 \][/tex]
Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Slopeequals6, passing through (negative 2,5)
Answers
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=6[x-(-2)]\implies y-5=6(x+2) \\\\\\ y-5=6x+12\implies y=6x+17\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
For 20 Points.
============
Answers
Answer:
D) 33
Step-by-step explanation:
The sum of the lengths of the segments is equal to the overall length:
(3x -5) + 8 = 4x -7
10 = x . . . . . . . . . . . . add 7-3x to both sides
Then the overall length is ...
MO = 4·10 -7 = 33
Answer:
Step-by-step explanation:
(3x -5) + 8 = 4x -7
10 = x what you wnat to do is add 7-3x to both sides
= 4·10 -7 = 33
and that should be your answer 33
NEED HELP QUICK!!!!Charmaine is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.
(a) How many revolutions does Charmaine make per foot of distance traveled?
(b) What is the slope of the graph?
Answers
Answer:
Step-by-step explanation:
Circumference of the wheel = (pi)d = 45*3.14 = 141.3 inches
----
Distance traveled in inches: 5*141.3 = 706.5 inches
---
Distance traveled in feet: 706.5/12 = 58.875 feet
A piece of thread is 52,000 nanometers thick. How many meters thick is the
thread? Write your answer in standard form.
1 nanometer = 1.0 x 10 meters
Answers
Answer:
0.000052
1 nanometer = .000000001 meters
.000000001 x 52000 = 0.000052
To convert 52,000 nanometers to meters, divide by the conversion factor of 1,000,000,000 nanometers per meter, resulting in a thickness of 5.2 x 10-8 meters in standard form.
To convert the thickness of a piece of thread from nanometers to meters, we need to use the conversion factor that 1 meter equals 1,000,000,000 nanometers, or 1 m = 109 nm.
Using this conversion factor, we can set up the following calculation:
Thickness in meters = Thickness in nanometers \/ Conversion factor
Thickness in meters = 52,000 nm \/ (109 nm/m)
Thickness in meters = 52,000 nm \/ 1,000,000,000 nm/m
Thickness in meters = 0.000000052 m or 5.2 x 10-8 meters when expressed in standard form.
Anthony is saving for a Xbox one he currently has the $165 saved and earned $40 per week doing chores around the house if an Xbox cost 500+10% sales tax how long will it take for him to save that amount
Answers
Answer:
10 weeks
Step-by-step explanation:
Let w represent the number of weeks Anthony will be saving. Then he wants ...
165 + 40w = 500 +0.10×500
40w = 385 . . . . . subtract 165 and simplify
w = 9.625 . . . . . . divide by 40
It will take Anthony 9.625 ≈ 10 weeks to save that amount.
The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t − 1.5t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?
Answers
Answer:
20 seconds
Step-by-step explanation:
Given:
Position of car = s(t) = 60t-1.5t^2
The speed is the change in position.
So,
[tex]Speed\ of\ car=\frac{ds}{dt} = \frac{d}{dt} (60t) -\frac{d}{dt} (1.5t^2)\\=60-2t(1.5)\\=60-3t[/tex]
When the car will stop, the speed will be zero.
[tex]60-3t=0\\3t=60\\t = \frac{60}{3}\\ t=20[/tex]
Therefore, the car will stop after 20 seconds of applying the break ..
Julio uses 3/4 cups of honey to make a batch of granola bars. Julio used 7 1/2 cusp of honey when he made some granola bars yesterday.
Write an equation that models this situation, using x to represent the number of batches of granola bars julio made.
How many batches of gronola bars did julio make?
Please Show work
Answers
Answer:
[tex]8\frac{2}{8}[/tex]
Step-by-step explanation:
x = number of granola bars
[tex]\frac{3}{4} + 7\frac{1}{2} = \frac{6}{8} + 7\frac{4}{8} = 7\frac{10}{8} = 8\frac{2}{8}[/tex] = x[/tex]
Solve the equation