Answer:
y = -1/2x - 3
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Determine known variables
Slope = -1/2 (m = -1/2)
y-intercept - (0, -3), so b = -3
Step 2: Write in known variables
y = -1/2x - 3
Find the equation of a line that passes through the point (4,2) and has a gradient of -2. Leave your answer in the form y=mx+c
Answer:
y = - 2x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c
to find c substitute (4, 2 ) into the equation
2 = - 8 + c ⇒ c = 2 + 8 = 10
y = - 2x + 10 ← equation of line
Answer:
y = - 2x + 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c
To find c we must substitute (4, 2 ) into the equation
2 = - 8 + c, c = 2 + 8 = 10
y = - 2x + 10
On a map scale, I inch = 53 miles. Two attractions are eight inches apart on the map. How far are they apart in miles?
Answer:
424 miles
Step-by-step explanation:
53 x 8 = 424 miles
9 athletes from a high school weightlifting team were randomly selected to begin a new resistance weight program. After 8 weeks, the difference in how much weight they could lift (after - before) was recorded below in kg 4, 13.5, 15, 6, 12, 14, 19.5, 7.5, 13, Assume the population distribution is approximately normal. Find a 95% confidence interval for the mean strength gain of all students from this school if they joined the program.
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the mean strength gain of all students from this school if they joined the program is (7.85, 15.37).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 9 - 1 = 8 df, is t = 2.306.
The other parameters are given as follows, with the help of a calculator.
[tex]\overline{x} = 11.61, s = 4.89, n = 9[/tex]
Hence:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 11.61 - 2.306\frac{4.89}{\sqrt{9}} = 7.85[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 11.61 + 2.306\frac{4.89}{\sqrt{9}} = 15.37[/tex]
The 95% confidence interval for the mean strength gain of all students from this school if they joined the program is (7.85, 15.37).
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A 5 cm object is 18. 0 cm from a convex lens, which has a focal length of 10. 0 cm. What is the distance of the image from the lens? Round your answer to three significant figures. Cm What is the height of the image? Round your answer to three significant figures. Cm.
The distance of the image from the lens V=22.5cm and the height of the image h=6.25cm.
What will be the distance and the height of the image placed in front of the convex lens?
It is given that
Hieght of an object H = 5cm
Distance of an object =18cm
Focal lenght of lens = 10cm
As we know that the lens formula is given by
[tex]\dfrac{1}{f} =\dfrac{1}{v} +\dfrac{1}{u}[/tex]
[tex]\dfrac{1}{v} =\dfrac{1}{10} -\dfrac{1}{18}=\dfrac{8}{180}[/tex]
so now
[tex]v= \dfrac{180}{8} =22.5\ cm[/tex]
Now to find the height of the image
[tex]\rm magnification =\dfrac{v}{u} =\dfrac{-Image\ Hieght }{object\ height}[/tex]
[tex]\rm magnification =\dfrac{22.5}{18} =\dfrac{-x}{5}[/tex]
[tex]x=-6.25\ cm[/tex]
Thus the distance of the image from the lens is V=22.5cm and the height of the image h=6.25cm.
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Solve the following system of equations graphically on the set of axes below.
y = 2x – 1
x + 3y = 18
Answer:
(x, y) = (3, 5)
Step-by-step explanation:
To solve these equations graphically, you plot each one, then identify the coordinates of the point of intersection.
The first equation can be graphed using the y-intercept of -1 and the slope of 2.
The second equation has a y-intercept of 18/3 = 6, and a slope of -1/3. The x-intercept of 18 is off the chart, so the slope and intercept are a good way to plot this line, too.
__
The slope is the "rise" divided by the "run". A slope of 2 means the line goes up 2 units for each unit to the right. A slope of -1/3 means the line goes down 1 unit for each 3 units to the right.
The solution is (x, y) = (3, 5).
Write −x^2+2xy−y^2 as the opposite of the square of a binomial.
PLEASE HELP ME PLEASE I WILL GIVE BRAINLYEST
Answer:
[tex]-(x-y)^2[/tex]
Step-by-step explanation:
Original expression:
[tex]-x^2+2xy-y^2[/tex]
Factor out -1:
[tex]\implies -(x^2-2xy+y^2)[/tex]
Factor [tex]x^2-2xy+y^2[/tex]:
[tex]\implies -(x-y)(x-y)[/tex]
Apply exponent rule [tex]aa=a^2[/tex]:
[tex]\implies -(x-y)^2[/tex]
(a) Complete the table.
There are 18 red counters in the bag.
(b) Work out the total number of counters in the bag.
Answer:
a) Red = 0.2 Blue= 0.4 and White =0.4
b) 90 counters in total
Step-by-step explanation:
a)Firstly we know that the probability of mutually exclusive events is equal to 1 and the question states that the probability of blue and white counter is the same so we subtract 1-0.2 = 0.8 and we divide that by 2 as a result 0.4 .
b) P= Favourable outcomes / total number of outcomes
P(red) = 0.2
total number of red counters = 18
0.2 = 18/t cross multiplying have 0.2t= 18
Dividing throughout by 0.2 having 90
Which segments are congruent? eh and ef gh and fe fg and eh ef and gf
If the two sides of the triangle are equal then these two triangles are similar. The sides EF and GF are congruent to each other. Then the correct option is D.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
In ΔEDF and ΔGDF
DF = DF = radius (common side)
ED = GD = radius
If the two sides of the triangle are equal then these two triangles are similar.
Thus, EF and GF are congruent to each other.
More about the triangle link is given below.
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Answer:
the answer is D
Step-by-step explanation:
EF and GF
Express as a sum :
15-7
PLS HELP WILL MARK BRAINLIST
The distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30°. the light forms a second-order bright band. how large is the path difference? 1047 nm 1571 nm 3142 nm 6284 nm
The path difference if the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30° is 1.57 × 10⁻⁶ m.
What is constructive interference?When the maxima of two waves add up (the two waves are in phase), the amplitude of the resultant wave equals the total of the separate amplitudes, this is known as constructive interference.
We know that for constructive interference, therefore, the formation of bright fringe through a diffraction grating is given by:
d sin θ = n λ
where d is the distance between slits, θ is the angle of diffraction, n is the order of fringe, and λ is the path difference.
As it is given that the distance between slits on a diffraction grating is 0.60 mm, and one of the angles of diffraction is 0.30°, therefore, the path difference can be written as,
[tex]\begin{aligned}\lambda &= \dfrac{(d sin \theta)}{ n} \\\\&=\dfrac{0.60 \times 10^{-3 }m) \times sin (0.30)}{2}\\\\ &= 1.57 \times 10^{-6}\rm\ m\end{aligned}[/tex]
Hence, the path difference is 1.57 × 10⁻⁶ m.
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Help please! This is an assignment!
HELP PLEASE ASAP. I really need help so it would be amazing if you could help me.
Answer:
ans at lower left
Step-by-step explanation:
scale up every element in the matrix in the question by 2 will get you the ans.
5/4 × (3 × 1/4 I NEED HELP
Answer: 15/16
Step-by-step explanation:
5/4 * (3 * 1/4) =
Mutiply 3 * 1/4
5/4 * 3/4 =
Mutiply 5/4 * 3/4
5/4 * 3/4 = 15/16
Answer:
[tex]\frac{15}{16}[/tex]
Step-by-step explanation:
[tex]\frac{5}{4}\cdot \:3\cdot \frac{1}{4}[/tex]
[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:3=\frac{3}{1}[/tex]
[tex]=\frac{5}{4}\cdot \frac{3}{1}\cdot \frac{1}{4}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\frac{5\cdot \:3\cdot \:1}{4\cdot \:1\cdot \:4}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:5\cdot \:3\cdot \:1=15[/tex]
[tex]=\frac{15}{4\cdot \:1\cdot \:4}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:1\cdot \:4=16[/tex]
[tex]\frac{15}{16}[/tex]
Hence, 15/16 is the correct Answer.
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The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentage
If their wage went from $6.80 to $10.19 in 7 years what is the doubling time?
(nearest year)
The doubling time of the hourly wage of the workers is an illustration of an exponential function that has a rate of 2
The doubling time of the wage is 4 years
How to determine the doubling timeA doubling function is represented as:
[tex]p = w \times 2^{\frac{x}{t}}[/tex]
Where:
p represents the final amount i.e. p = 10.19w represents the initial amount i.e. w = 6.80t represents the duration i.e. t = 7x represents the doubling timeSo, we have:
[tex]10.19 = 6.80 \times 2^{\frac{x}{7}}[/tex]
Divide both sides by 6.80
[tex]1.50 = 2^{\frac{x}{7}}[/tex]
Take the logarithm of both sides
[tex]\log(1.50) = \log(2^{\frac{x}{7}})[/tex]
Apply the law of logarithm
[tex]\log(1.50) = \frac{x}{7}}\log(2)[/tex]
Multiply both sides by 7
[tex]7 \times \log(1.50) = x\log(2)[/tex]
Divide both sides by log(2)
[tex]x = 7 \times \log(1.50) \div \log(2)[/tex]
[tex]x = 4.09[/tex]
Approximate
[tex]x \approx 4[/tex]
Hence, the doubling time is 4 years
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Two hot-air balloons, one red and one blue, took off at the same time from different platforms. Each began ascending at a constant rate.
The following equation gives the height (in meters) of the red hot-air balloon as a function of time (in seconds).
h = \dfrac{1}{2} t + 4h=
2
1
t+4h, equals, start fraction, 1, divided by, 2, end fraction, t, plus, 4
The height (in meters) of the blue hot-air balloon as a function of time (in seconds) is given by the following table of values:
\text{Time}Timestart text, T, i, m, e, end text (seconds) \text{Height}Heightstart text, H, e, i, g, h, t, end text (meters)
444 555
666 666
888 777
Which balloon started at a greater height?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
The red one
(Choice B)
B
The blue one
(Choice C)
C
They both started at the same height
Which balloon ascended faster?
Lucy's school is selling 100 raffle-tickets to raise money for a new gymnasium. The grand-prize is a ten-speed mountain bike. Which word or phrase describes the probability that she will win the raffle if she buys 0 tickets?
\text{likely}likely
\text{unlikely}unlikely
\text{an equal chance or 50-50}an equal chance or 50-50
\text{impossible}impossible
attempt 1 out of 2
Tionna McGirt
Probability Language Level 1
Mar 21, 1:52:28 PM
Lucy's school is selling 100 raffle-tickets to raise money for a new gymnasium. The grand-prize is a ten-speed mountain bike. Which word or phrase describes the probability that she will win the raffle if she buys 0 tickets?
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A circle is represented by the equation x2 + 8x + y2 – 12y = –29. Describe the algebraic technique(s) needed to rewrite the equation in standard form. Identify the center and radius of the circle. Show your work
The equation of the circle can be written in standard form and in a general form
The center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]
How to identify the radius and the center of the circleThe equation of the circle is given as:
[tex]x^2 + 8x + y^2 - 12y = -29[/tex]
Rewrite as:
[tex]x^2 + 8x + k - k + y^2 - 12y + k - k= -29[/tex]
Express k as the square of the half of the coefficients of x and y.
So, we have:
[tex]x^2 + 8x + (4)^2 - (4)^2 + y^2 - 12y + (6)^2 - (6)^2= -29[/tex]
Evaluate the exponents
[tex]x^2 + 8x + 16 - 16 + y^2 - 12y + 36 - 36 = -29[/tex]
Collect like terms
[tex]x^2 + 8x + 16 + y^2 - 12y + 36 = -29 + 16 + 36[/tex]
Express as perfect squares
[tex](x + 4)^2 + (y - 6)^2 = -29 + 16 + 36[/tex]
[tex](x + 4)^2 + (y - 6)^2 = 23[/tex]
The standard equation of a circle is:
[tex](x - a)^2 + (y - b)^2 + r^2[/tex]
Where:
Center = (a,b)
Radius = r
So, we have:
Center = (-4,6)
Radius = [tex]\sqrt{23[/tex]
Hence, the center of the circle is (-4,6) and the radius is [tex]\sqrt{23[/tex]
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A point at (54, -27) is rotated 720° clockwise about the
origin. What are the new coordinates for the point?
a. (54,-27)
b. (-27, -54)
c. (-54, 27)
d. (27,54)
Write a function rule for the table.
Answer:
C. p = h + 16
Step-by-step explanation:
Eduardo is making a friendship bracelet with 6 different colors of thread. He uses 22 inches of each color. How many feet of thread does he use in all?
You move up 5 units. You end at (3, 9). Where did you start?
Answer:
You started at (3, 4)
4 + 5 = 9, the only option to get there in this case.factorized, 3 x 3(x) and replace for y.Jameelah got 4 kilograms of candy. Since she didn’t want to eat it all, she decided to share it with her 4 friends. If the 5 of them share the 4 kilograms, how much will each of them have?
help me
Answer:
Each of them will have 0.8 kg of the candy.
Step-by-step explanation:
Don't have one sorry!
In a football club there are 2 balls for every 12 players. How many footballs will
be needed for 48 players?
Answer:
8
Step-by-step explanation:
Given:
In a football club there are 2 balls for every 12 players.To Find:
How many footballs will be needed for 48 players?
Solve:
Since there are 2 balls for every 12 players..
Let's b = balls and P = Players
2b = 12p
4b = 24p
6b = 36p
8b = 48
Hence, we can conclude that there will be 8 footballs needed for 48 players
~Learn with Lenvy~
Answer:
8 balls
Step-by-step explanation:
We can use ratios to solve.
2 balls x balls
------------- = -----------------
12 players 48 players
Using cross products
2 * 48 = 12 *x
96 = 12x
Divide each side by 12
96/12 =12x/12
8=x
They needs 8 balls
A gymnastics coach records the scores of a gymnast and develops the probability distribution below. what is the probability the gymnast scores a 9 or 9.5? probability distribution gymnastics score: x probability: p(x) 5 0.02 5.5 0.02 6 0.06 6.5 0.1 7 0.16 7.5 0.14 8 0.18 8.5 0.18 9 ? 9.5 0.02 0.02 0.04 0.12 0.14
The sum of all the probabilities must be one. Then the probability that the gymnast scores a 9 or 9.95 is 0.14.
What is a probability distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
Researching on the internet, the probability of the gymnast getting each score is given by:
P(X = 5) = 0.02P(X = 5.5) = 0.02P(X = 6) = 0.06P(X = 6.5) = 0.1P(X = 7) = 0.16P(X = 7.5) = 0.14P(X = 8) = 0.18P(X = 8.5) = 0.18P(X = 9) = xP(X = 9.5) = 0.02Considering that it is a distribution, the sum of all the probabilities must be one.
0.02 + 0.02 + 0.06 + 0.1 + 0.16 + 0.14 + 0.18 + 0.18 + x + 0.02 = 1
0.88 + x = 1
x = 0.12
The probability that the gymnast scores a 9 or 9.95 will be
P(9 or 9.5) = (X = 9) + P(X = 9.5) = 0.12 + 0.02 = 0.14
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Answer: D
Step-by-step explanation:
trust me bro I got it right
A coat and a pair of boots are on sale for 20% off. The regular price of the coat is $225. The regular price of the boots is $130. Part A find the sale price of the coat —————-Part B what is the sale price of the boots?
Answer:
Part A = $180
Part B = $104
Step-by-step explanation:
Part A:
You do 255÷5=51
51 x 4 = 180
Part B:
You do 130÷5=26
26 x 4 = 104
Answer:
$180 for the coat, $104 for the boots
Step-by-step explanation:
first: percent = decimal (20 = 0.20)
for the coat:
225-(225x0.20)
225-40 = 180
for the boots:
130- (130x0.20)
130-26 = 104
Which graph represents the solution set of the compound inequality?
−5
please help!!!
Answer:
the first
Step-by-step explanation:
it just is. Be smarter.
Find the size angle XYZ
Give your answer to 1 decimal place
Answer:
∠ XYZ ≈ 72.9°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan XYZ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{XY}[/tex] = [tex]\frac{13}{4}[/tex] , then
∠ XYZ = [tex]tan^{-1}[/tex] ( [tex]\frac{13}{4}[/tex] ) ≈ 72.9° ( to 1 dec. place )
The function y = 58. 7(1. 03)^t gives a country’s population, y (in millions), where t is the number of years since January 1994. According to this function, what was the approximate population of the country in January 2002
Answer:
Approximate population ≈ 74.36 million.
Step-by-step explanation:
The given problem involves modeling of an exponential growth or decay function of a population.
Definition:Exponential growth ( relative growth ) occurs when a population grows or increases exponentially by the same factor, over the same amount of time. Exponential decay occurs when a population decreases continuously by a constant factor, over the same amount of time.We can model the exponential growth of a population using the following Exponential Growth Model:
⇒ [tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex]Where:
P( t ) = population after "t" years P₀ = initial population r = relative growth rate; positive "r" value means that the population is increasing; negative "r" value implies that the population is decreasing. t = time (typically in years)Solution:Based from the given equation, [tex]\displaystyle\mathsf{y\:=\:58.7(1.03)^t }[/tex] , we can infer that:
⇒ [tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex] or [tex]\displaystyle\mathsf{y\:=\:P_0 (1\:+\:r)^t }[/tex]
Where:
P( t ) or y = population after "t" yearsP₀ = initial population = 58.7r = relative growth rate = 0.03 or 3% = the population is increasing (exponential growth).t = time (typically in years) = 8 years (difference between January 2002 and January 1994).Step 1: Substitute the given values into the Exponential Growth Model formula, and solve for P( t ) :
[tex]\displaystyle\mathsf{P(t)\:=\:P_0 (1\:+\:r)^t }[/tex]
⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1\:+\:.03)^8 }[/tex]
Step 2: Follow the order of operations, addition inside the parenthesis:
⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.03)^8 }[/tex]
Step 3: Follow the order of operations, applying the exponent into the parenthesis (do not round off the digits inside the parenthesis):
⇒ [tex]\displaystyle\mathsf{P(8)\:=\:58.7 (1.266770081) }[/tex]
Step 4: Follow the order of operations, multiplying 58.7 (P₀) into the parenthesis:
⇒ [tex]\displaystyle\mathsf{P(8)\:\approx \:74.35940378\quad or \quad 74.36\:\:million}[/tex]
Final Answer:Therefore, the approximate population of the country in January 2002 is 74.36 million.
________________________Keywords:Exponential functions
Exponential growth
Exponential decay
Exponential growth model
____________________________
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Need it sooner than later
A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males.
Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)
Using the z-distribution, as we are working with a proportion, it is found that:
A. The 98% confidence interval is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.
B. Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.
What is the mean and the standard error for the distribution of differences?For each sample, they are given by:
[tex]p_F = \frac{53}{150} = 0.3533, s_F = \sqrt{\frac{0.3533(0.6467)}{150}} = 0.039[/tex]
[tex]p_M = \frac{89}{275} = 0.3236, s_M = \sqrt{\frac{0.3236(0.6764)}{275}} = 0.0282[/tex]
Hence, for the distribution of differences:
[tex]p = p_F - p_M = 0.3533 - 0.3236 = 0.0297[/tex]
[tex]s = \sqrt{s_F^2 + s_M^2} = \sqrt{0.039^2 + 0.0282^2} = 0.048[/tex]
What is the confidence interval:It is given by:
[tex]p \pm zs[/tex]
98% confidence interval, hence, using a z-distribution calculator, the critical value is of z = 2.327.
Then:
[tex]p - zs = 0.0297 - 2.327(0.048) = -0.082[/tex]
[tex]p + zs = 0.0297 + 2.327(0.048) = 0.141[/tex]
The 98% confidence interval is (-0.082, 0.141), and it means that we are 98% sure that the true difference of the population proportions are in this interval.
Item b:
Since 0 is part of the confidence interval, it does not give convincing evidence of a difference between the population proportions.
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Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
2, 5, 8, ...