Answer:
The y-intercept would be between 0 and -4 likely about -3.
Step-by-step explanation:
The y-intercept would be between 0 and -4 likely about -3.
Since the parabola has an axis of symmetry at x = 1 and a minimum of y = -4 then the vertex is (1,-4).
It has an x-intercept at x = -1 or (-1,0). This means from the vertex up to the x-intercept the function has to cross through the y-axis. This makes the y-intercept between 0 and -4 and likely at -3.
The y-intercept of the quadratic function given above is found to be at y = -3. This conclusion is reached by analyzing the vertex, its symmetry, and x-intercepts of the function, and applying these properties in the standard form of a quadratic function.
Explanation:The subject of this question is the properties of a quadratic function in mathematics. The given characteristics provide us with enough information to determine the y-intercept of the function. Let's analyze the information.
Since the axis of symmetry is 'x = 1', we know that the vertex of the parabola is at (1, y). Also, because it has a minimum value of 'y = -4', we know the y-coordinate of the vertex is -4. Therefore, the vertex of the parabola is at (1, -4).
An x-intercept at 'x = -1' means that (-1, 0) is a point on the parabola. From the nature of the symmetry of parabolas, we know that if there is a point (a, 0) on the parabola, there will also be a point on the other side of the axis of symmetry at (2h-a, 0), where 'h' is the x-coordinate of the vertex. So, we can calculate the other x-intercept as (2*1 - (-1), 0), which gives us (3, 0). Thus, a point on the parabola is also (3, 0).
Equipped with the vertex (1, -4) and a point on the parabola (3,0), we can use the form of a quadratic function y = a(x-h)² + k to determine the quadratic function. Substituting coordinates of the vertex into the formula for h and k, and the coordinates of the point into the formula for x and y, we get 0 = a(3-1)² + (-4). From that, we can solve for 'a', which equals 1.
So, our quadratic function is y = (x-1)² - 4. To find the y-intercept (the point where the function crosses the y-axis, where x=0), we substitute x=0 into our function, which yields y = (0-1)² - 4 = -3.
The y-intercept of the parabola is at y = -3.
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assume that random guesses are made for 8 multiple choice questions on an SAT test, so that there are n=9 trials, each with probability of success (correct) given by p=0.6. find the indicated probability for the number of correct answers. find the probability that the number x of correct answers is fewer than 4.
Answer:
[tex]P(x<4)=0.0994[/tex]
Step-by-step explanation:
If we call x the number of correct questions obtained in the 9 attempts, then:
x is a discrete random variable that can be modeled by a binomial probability distribution p, with n = 9 trials.
So, the p of x successes has the following formula.
[tex]P(x) =\frac{n!}{x!(n-x)!}*p^x(1-p)^{n-x}[/tex]
Where:
n = 9
p = 0.6
We are looking for P(x<4)
By definition:
[tex]P(x<4) = P(x\leq3) = P(0) + P(1) + P(2) +P(3)[/tex]
Then:
[tex]P(x\leq3)=\sum_{x=0}^{3} \frac{9!}{x!(9-x)!}*(0.6)^x(1-0.6)^{9-x}[/tex]
[tex]P(x\leq3)=0.0994[/tex]
Probabilities are used to determine the chances of an event
The probability that the number of correct answers is fewer than 4 is 0.0994
The given parameters are:
[tex]n = 9[/tex]
[tex]p =0.6[/tex]
The probability is a binomial probability, and it is calculated using:
[tex]P(x) = ^nC_x p^x (1 - p)^{n -x}[/tex]
Fewer than 4 means: x = 0, 1, 2 and 3
So, we have:
[tex]P(x<4) = ^9C_0 \times 0.6^0 \times (1 - 0.6)^{9 -0} +^9C_1 \times 0.6^1 \times(1 - 0.6)^{9 -1} +^9C_2 \times 0.6^2\times (1 - 0.6)^{9 -2} +^9C_3 \times 0.6^3\times (1 - 0.6)^{9 -3}[/tex]
This gives
[tex]P(x<4) = 1 \times 0.6^0 \times (1 - 0.6)^9 + 9 \times 0.6^1 \times(1 - 0.6)^8 +36 \times 0.6^2 \times (1 - 0.6)^7 +84 \times 0.6^3 \times (1 - 0.6)^6[/tex]
Using a calculator,
[tex]P(x<4) = 0.099352576[/tex]
Approximate
[tex]P(x<4) = 0.0994[/tex]
Hence, the probability that the number of correct answers is fewer than 4 is 0.0994
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How many decameters are there in 4.5 kilometers
There are 100 decameters (dam) in a kilometer (km).
4.5km x 100dam = 450 decameters
Answer: 450 decameters
Product A is an 8oz bottle of cough medication that sells for $1.36. Product B is a 16-oz. bottle of cough medication that costs $3.20. which product has the lower unit price?
Answer:
8 oz bottle
Step-by-step explanation:
1.36/8 = .17
3.20/16 = .20
Answer:
Product A
Step-by-step explanation:
You're going to use the sell price divided by bottle size.
Product A, $1.36/8, $0.17 per oz.
Product B, $3.2/16, $0.2 per oz.
therefore A is cheaper
ronen selects 75 random products to test their quality he found that 6 products had defects how many out of 3000 should ronen predict have defects
Answer: About 43
Step-by-step explanation:
in each 75 there is 6 mistakes so 75-6=69
then if you divide 3000 by 69 you get 43 im pretty sure
To predict the number of defective products out of 3000, Ronen can use proportions. He found 6 defects in a sample of 75 products, which scales up to approximately 240 defects in 3000 products.
Ronen found that 6 out of 75 products had defects in a random sample. To predict how many out of 3000 products would have defects, we can set up a proportion because we are assuming that the sample proportion will be representative of the larger population. Here's the step-by-step explanation:
First, establish the proportion of defective products in the sample: 6 defects / 75 products.Next, set this equal to x (the number we want to find) over 3000 products: 6/75 = x/3000.Cross multiply to solve for x: (6 * 3000) = (75 * x).Do the multiplication: 18000 = 75x.Finally, divide both sides by 75 to find x: 18000 / 75 = x.This calculates to 240. Therefore, Ronen can predict that approximately 240 out of 3000 products will have defects.
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the squares shares one side with the rectangle. The total area of the constructed figure is 120 cm2. What is the perimeter of the rectangle?
Answer:
The perimeter of rectangle is [tex]18\ cm[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
[tex]x=y+5[/tex] ----> equation A
[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)
substitute the equation A in equation B
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}[/tex]
[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]
using a graphing calculator -----> solve the quadratic equation
The solution is
[tex]y=2\ cm[/tex]
Find the value of x
[tex]x=y+5 ----> x=2+5=7\ cm[/tex]
Find the perimeter of rectangle
[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]
Retro Rides is a club for owners of vintage cars and motorcycles. Every year the club gets together for a ride. This year, 38 vehicles participated in the ride. The total number of tires of all the vehicles was 114. Assuming each car has 4 tires and each motorcycle has 2 tires, how many each of cars and motorcycles participated in the ride? A. 16 cars; 22 motorcycles B. 23 cars; 15 motorcycles C. 19 cars; 19 motorcycles D. 21 cars; 17 motorcycles
Answer:
C. 19 cars; 19 motorcycles
Step-by-step explanation:
Let c represent the number of cars and m represent the number of motorcycles that participated this year.
This year a total of 38 vehicles participated. So, we can write the equation as:
c + m = 38 (Equation 1)
Each car has 4 tires, so number of tires in c cars will be 4c.
Each motorcycle has 2 tires, so number of tires in m motorcycles will be 2m.
In total there were 114 tires, so we can set up the equation as:
4c + 2m = 114 (Equation 2)
From equation 1, m = 38 - c. Using this value in Equation 2, we get:
4c + 2(38 - c) = 114
4c + 76 - 2c = 114
2c = 114 - 76
2c = 38
c = 19
Using this value in equation 1, we get:
19 + m = 38
m = 19
Thus, 19 cars and 19 motorcycles participated in the ride.
Answer:
22 cars; 32 motorcycles
Step-by-step explanation:
I Did It On Study Island
Danny's office ordered a sandwich tray for lunch. The tray had 4 turkey sandwiches, 7 ham sandwiches, and 6 tuna sandwiches. If Danny randomly picked a sandwich off the tray without looking, what is the probability that he picked a ham sandwich? A. B. C. D.
Step-by-step explanation:
The total amount of sandwiches on the tray is 4+7+6. This makes 17. This will be the denominator of our fraction which we are going to use for the probability.
There are 7 ham sandwiches on the tray, therefore the probability that he will pick a ham sandwich is 7/17.
Brainliest? :)
Final answer:
The probability that Danny picked a ham sandwich is 7/17, since there are 7 ham sandwiches out of a total of 17 sandwiches on the tray.
Explanation:
The question is about calculating the probability that Danny picked a ham sandwich. To determine this, we count the total number of sandwiches and then count the number of ham sandwiches.
Total number of sandwiches = 4 turkey + 7 ham + 6 tuna = 17 sandwiches.
Since there are 7 ham sandwiches, the probability (P) that Danny picks a ham sandwich is calculated by dividing the number of ham sandwiches by the total number of sandwiches.
P(ham sandwich) = Number of ham sandwiches / Total number of sandwiches
P(ham sandwich) = 7 / 17
Therefore, the probability that Danny picked a ham sandwich is 7/17.
HELP!!!!!! Determine the equation of the line with slope −4 that passes through the point M(−2, 1).
Answer:
y = -4x - 7Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope m = -4 and the point M(-2, 1).
The equation of a line:
[tex]y=-4x+b[/tex]
Put the coordinates of the point M to the equation of a line:
[tex]1=-4(-2)+b[/tex]
[tex]1=8+b[/tex] subtract 8 from both sides
[tex]-7=b\to b=-7[/tex]
Finally:
[tex]y=-4x-7[/tex]
Find the values of x and y. Leave answers in simplest radical form.
[tex] \sin(60°) = \frac{x}{14} \Leftrightarrow x = 14 \sin(60°) = \frac{14 \sqrt{3} }{2} = 7 \sqrt{3} \\ \cos(60°) = \frac{y}{14} \Leftrightarrow y = 14\cos(60°) = \frac{14}{2} = 7[/tex]
To factor the expression x³ - y³ into factors of the lowest possible order, we can use the formula for factoring a difference of cubes: a³ - b³ = (a - b)(a² + ab + b²). In this case, we have x³ - y³, so our factors are (x - y)(x² + xy + y²). These are the factors using complex coefficients.
Explanation:To factor the expression x³ - y³ into factors of the lowest possible order, we can use the formula for factoring a difference of cubes: a³ - b³ = (a - b)(a² + ab + b²). In this case, we have x³ - y³, so our factors are (x - y)(x² + xy + y²).
These are the factors using complex coefficients. To find the factors using real coefficients, we can use the fact that a complex conjugate pair of roots will always have real coefficients. Therefore, the factors using real coefficients will be (x - y)(x² + xy + y²).
Are the following equations (1,2,3) one solution, infinitely many solutions, or no solution for each one? Please and Thank You
1.
y-3x=5
y=3x+5
2.
y=6x+2
y=6x-2
3.
y=5x+9
y=3x-2
1.when you change the first equation to the form it is the same as the second which means infinite solutions
y-3x=5 --->y=3x+5 then set them equal to find many possible solutions
2.this is no solution because the slopes are the same when you combine these equation the 2's cancel out and you ar left with y=12x which cannot be solved
3.when everything is different there is one solution
find the difference of the given polynomials (8x^2-3x+1/3)-(2x^2-8x+3/5)
Answer:
[tex]\boxed{\bold{6x^2+5x-\frac{4}{15}}}[/tex]
Explanation:
[ Step One ] Remove Parenthesis: (a) = a
[tex]\bold{8x^2-3x+\frac{1}{3}-\left(2x^2-8x+\frac{3}{5}\right)}[/tex]
[ Step Two ] Simplify: [tex]\bold{-\left(2x^2-8x+\frac{3}{5}\right): \ -2x^2+8x-\frac{3}{5}}[/tex]
[tex]\bold{8x^2-3x+\frac{1}{3}-2x^2+8x-\frac{3}{5}}[/tex]
[ Step Three ] Simplify [tex]\bold{8x^2-3x+\frac{1}{3}-2x^2+8x-\frac{3}{5}: \ 6x^2+5x+\frac{1}{3}-\frac{3}{5}}[/tex]
[tex]\bold{6x^2+5x-\frac{4}{15}}[/tex]
[ [tex]\boxed{\bold{Final \ Answer}}[/tex] ]
➤ [tex]\bold{6x^2+5x-\frac{4}{15}}[/tex]
[tex]\boxed{\bold{Mordancy}}[/tex]
Explain how to write a linear equation for a line on a graph.
Use y = mx + b.
m represents the slope of the line.
the slope equals rise over run.
in other words, count the number of vertical and horizontal units from one point to another point on the line.
if you have the y-intercept and a point, you can also solve for m.
b represents the y-intercept.
find the point on the graph where x = 0.
b is the value of y.
for example, if the y-intercept was (0,4) then b would equal 4.
x and y represent a point on the graph.
pick any point on the graph and plug it in.
for example, if the point (1,2) is on the graph then x = 1 and y = 2.
Hanley made a scale drawing of his rectangular patio for a landscaping project. In the drawing, he used a scale of 1 inch = 5 feet. The dimensions of the patio in the scale drawing are 5.5 inches by 4 inches. What is the actual area of the patio?
A. 22 square feet
B. 95 square feet
C. 110 square feet
D. 550 square feet
Answer:
D 550 ft²
Step-by-step explanation:
5.5 x 5 = 27.5
4 x 5 = 20
A = LW
27.5 x 20 = 550
Scaling is the process in which the dimension of an object is multiplied or increased by the same ratio. The actual area of the rectangular patio is 550 feet².
What is scaling?Scaling is the process in which the dimension of an object is multiplied or increased by the same ratio.
As it is given that the ratio by which the patio is scaled is 1 inch = 5 feet. Therefore, a single inch on the drawing is 5 feet in the real world.
Now, the dimensions of the patio on the scale drawing are 5.5 inches by inches, therefore, each of the dimensions will be scaled.
[tex]\text{Length of the Patio}= 5.5\rm \times 5 = 27.5\ feet[/tex]
[tex]\text{Width of the Patio} = 4 \times 5 = 20\rm\ feet[/tex]
Further, the area of the rectangle is the product of its length and its breadth, therefore, the area of the rectangular patio is
[tex]\text{Area of the Patio} = Length \times Breadth\\[/tex]
[tex]= 27.5 \times 20\\\\= 550\rm\ feet^2[/tex]
Hence, the actual area of the rectangular patio is 550 feet².
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Convert 3.2 grams to milligrams.
0.0032 mg
32 mg
320 mg
3,200 mg
Answer:
3200
Step-by-step explanation:
multiply the mass value by 1000
Answer:
3,200 WILL BE YOUR ANSWER
Step-by-step explanation:
I HOPE 6THAT HELPS
Plz help !!!!!!!!!!!!!!
Answer: a) 21
Step-by-step explanation:
2A - 3B ; A = 6, B = -3
2(6) - 3(-3)
= 12 - -9
= 12 + 9
= 21
Simplify 4(1/2 + 5/4)+ -5
Answer:
2
Step-by-step explanation:
Hopefully this helps.
if a patient checks in at at 1:25 and seen at 1:54. how long did patient wait in waiting area?
Answer: " 29 minutes. "
_____________________________________________
Step-by-step explanation:
_____________________________________________
54 minutes (minus) 25 minutes =
54
- 25
_____________________________________________
29 minutes.
_____________________________________________
Answer 29 minutes
step by step solution:
patient seen at = 1:54
patient check in at = 1:25
waiting time= 1:54 - 1:25= 0: 29
Round 8.077 to nearest thousand
Answer:
Your answer is 8,077
Step-by-step explanation:
What you do is you take 8.077 and times it by 1,000.
8.077*1,000=8,077 as your answer.
Answer:
It equals 0, I hope this helps yoU!
Each week, Kelly pays $68.45 in federal income tax, $22.81 in state income tax, and $18.75 in other taxes. Which is the best estimate for the payroll tax Kelly pays each month?
Kelly's estimated monthly payroll tax is $475.94, which is found by adding together all of her weekly taxes and then multiplying by the average number of weeks in a month.
Explanation:To estimate the amount of payroll tax Kelly pays each month, we first need to find out how much she pays weekly and then multiply it by the number of weeks in a month on average.
Firstly, we add together all of the weekly taxes she pays, which includes federal income tax ($68.45), state income tax ($22.81), and other taxes ($18.75). The sum equals $110.01.
Then, to convert this weekly tax to a monthly estimation, we multiply by an average of 4.33 weeks in a month (since not every month is precisely 4 weeks). Therefore, $110.01 * 4.33 is approximately $475.94.
Therefore, the best estimation for the monthly payroll tax that Kelly pays is $475.94.
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Write 31 in tens and ones
Answer:
3 tens and 1 ones
Step-by-step explanation:
3 tens would be
3 x 10
which is 30
and 1 one is 1
30 + 1 = 31
Hope this helps! Please mark Brainliest! Thanks!!
Please help!!!!! Will give brainliest!!!
See the attached picture:
what is the value of X? show all of your work
Answer:
x = 5 cmStep-by-step explanation:
Use the Pythagorean theorem:
[tex]AB^2+BC^2=AC^2[/tex]
We have
[tex]AB=8\ cm,\ BC=x\ cm,\ AC=\sqrt{89}\ cm[/tex]
Substitute:
[tex]8^2+x^2=(\sqrt{89})^2\qquad\text{use}\ (\sqrt{a})^2=a\ \text{for}\ a\geq0\\\\64+x^2=89\qquad\text{subtract 64 from both sides}\\\\x^2=25\to x=\sqrt{25}\\\\x=5\ cm[/tex]
What is the measure of ∠L ? A right triangle L M N. Angle M is marked as a right angle. Side L M is labeled as 18 inches. Side L N is labeled as 60 inches.
Answer:
72.54°
Step-by-step explanation:
Given that triangle LMN is a right-angle triangle and LM=18 inches and LN =60 inches then;
applying the cosine rule
cos ∠L=Adjacent/hypotenuse
cos∠L=18/60
cos∠L=0.3
cos⁻¹ ∠L= 72.54°
Answer:
72.54°
Step-by-step explanation:
Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y=e^x, x=1, and y=1 is revolved around the line y=-2?
The fourth option is correct.
See the attached image. The red cylinder represents a washer formed by the described revolution. Its volume is
[tex]\pi((\text{outer radius})^2-(\text{inner radius})^2)(\text{height})[/tex]
so when we integrate, we take
[tex]\displaystyle\pi\int_0^1((e^x+2)^2-3^2)\,\mathrm dx[/tex]
is the function linear or non-linear?
Answer:
Linear
Step-by-step explanation:
It is linear because it is a straight line.
Answer:
Linear
Step-by-step explanation:
The function is linear because it is a straight line.
one day reeva baked several dozen muffins. the next day she made 8 dozen more muffins. if she made 20 dozen muffins in all, how many dozen did she make the first day?
Answer: 12 Dozens of Muffins
Step-by-step explanation:
An easy way to do this is to work backwards. 20(Total number of muffins) - 8(Muffins made in the second day) = 12(Muffins made in the first day) that means that she made 12 dozens, or a dozen dozens!
The temple at the top of the pyramid is approximately 24 meters above the ground, and there are 91 steps leading up to the temple. How high above the ground would you be if you were standing on the 50th step?
Answer:
[tex]13.19\ m[/tex]
Step-by-step explanation:
step 1
Divide the total height by the number of step leading
[tex]\frac{24}{91}=0.2637\frac{m}{step}[/tex]
step 2
Multiply [tex]0.2637\frac{m}{step}[/tex] by 50 step
[tex]0.2637(50)=13.19\ m[/tex]
If you were standing on the 50th step of the pyramid, you would be approximately 13.185 meters above the ground, calculated by finding the height per step and multiplying by the number of steps climbed.
Explanation:The task is to calculate how high above the ground you would be if you were standing on the 50th step of a pyramid that has a temple approximately 24 meters above the ground with a total of 91 steps leading up to the temple. To solve this, we will assume that the height the steps cover (24 meters) is evenly distributed across the number of steps (91). So, each step represents 24 meters divided by 91 steps in height.
First, let's calculate the height of each step:
Height per step = Total height / Number of steps
Height per step = 24 meters / 91 steps ≈ 0.2637 meters per step
Next, we need to calculate the height at the 50th step:
Height at 50th step = Height per step * Number of steps climbed
Height at 50th step = 0.2637 meters per step * 50 steps ≈ 13.185 meters
Therefore, if you were standing on the 50th step, you would be approximately 13.185 meters above the ground.
how do finde the volum of a circel
Answer:
hi there
your answer to this is:
by using the equation πr² . the R is the Radius of the circle. then multpitly by it the base of the circle.
I hope this helps you out
Have a great Morning
FaithRawlins14
Final answer:
The term 'circle' does not represent a 3D object with volume. For calculating volume, one must consider 3D shapes like cylinders or spheres which do have volume; their volumes are calculated using the formulas V = πr²h for cylinders, and V = 4/3 πr³ for spheres, respectively.
Explanation:
It seems there is a confusion in the question as a 'circle' is a 2D shape and does not have volume. However, if we are referring to a cylinder which has a circular base, then the volume can be calculated. To find the volume of a cylinder, we use the formula V = πr²h, where V represents volume, π is approximately 3.142, r is the radius of the circular base, and h is the height of the cylinder.
In the case of a sphere, a 3D object that could be mistaken as a 'circle' in conversations, the volume formula is given by V = 4/3 π r³. This is derived from geometric principles, ensuring the units match, and considering the sphere's volume in relation to a cube that would contain it. Applying this to an example, the volume of a sphere with a radius of 4.30 inches can be converted to cubic centimeters, and would be calculated using the volume formula for a sphere.
When 1,250^3/4 is written in simplest radical form, which value remains under the radical?
A. 2
B. 5
C. 6
D. 8
Terrence randomly sampled 400 people and asked them if they prefer spring or fall. The results of his sample yielded an estimated population proportion of 43% who prefer spring. Deena randomly sampled 1,200 people and asked them if they prefer spring or fall. The results of her sample also yielded an estimated population proportion of 43% who prefer spring.
If Terrence and Deena use the same confidence level, which statement best describes the results of their margin of error calculations?
Terrence’s margin of error will be exactly three times as large as Deena’s.
Deena’s margin of error is half the amount of Terrence’s.
If Terrence samples 800 more people, his margin of error will be the same as Deena’s.
If Deena samples 400 fewer people, her margin of error would be exactly half the amount of Terrence’s.
on edge it's C. If Terrence samples 800 more people, his margin of error will be the same as Deena’s.
Answer:
Step-by-step explanation:
Margin of error is calculated as
Critical value multiplied by Std error of sample
= Critical value multiplied by square root of (variance/sample size)
Hence Margin of error
=[tex]z/t*(\frac{\sigma}{\sqrt{n} } )[/tex]
Thus square root of n is inversely proportion to margin of error.
Thus we have margin of error of Terrena would be square root of 3 times that of Deena
Thus option a, b and d are wrong
C is right because when sample sizes equal, the margin of error also would be equal.