The vertex form equation of the parabola whose vertex is; (2, -5) as required in the task content is; y = -(x - 2) - 5.
What is the vertex form equation of the parabola whose vertex is; (2, -5)?It follows from the task content that the vertex form equation of the parabola described in the task content is to be determined.
Since the vertex form equation of a parabola takes the form;
y = a (x - h)² + k
where the graph opens upward when a > 0 and opens downward when a < 0.
Therefore, the required vertex form equation of the parabola is; y = -(x - 2) - 5.
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A pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%, what is the total amount paid for the jeans?
The total amount that a customer will pay for the jeans is $33.696.
How to calculate the value?From the information given, pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%,
The value of the sales tax will be:
= Sales percentage × Amount
= 5.3% × $32
= $1.696
The total amount paid will be:
= Cost + Tax
= $32 + $1.696
= $33.696
The amount is $33.696.
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what is the slope of a line that passes through the points (-1, -3) and (-19,-18)
The slope of the line that passes through the points (-1, -3) and (-19,-18) is 16/17.
slope of a line :
the measurement of a line's direction in a coordinate plane.It is denoted by m.m = (y₂ - y₁)/(x₂ - x₁)m = tanθA = (x₁, x₂) = (-1, -3)
B = (y₁, y₂) = (-19,-18)
The slope of a line is given as :
slope = (y₂ - y₁)/(x₂ - x₁)
slope = (-19 - (-3))/(-18 - (-1))
slope = (-19 + 3)/(-18 + 1)
slope = ( -16 )/ ( -17)
slope = 16/17.
The slope of the line that passes through the points (-1, -3) and (-19,-18) is 16/17.
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OBFW Publishers
The Graduate Record Examinations (GRES) are widely used to help predict the performance of applicants to graduate schools.
The scores on the GRE Chemistry test are approximately normal with mean 694 and standard deviation 112.
(a) About what percent of test takers earn a score less than 500 on the GRE Chemistry test?
(b) What proportion of test takers earn a score greater than or equal to 900 on this test?
(c) Estimate the score at the 99th percentile on the GRE Chemistry test.
a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.
b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.
c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.
To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.
(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.
z-score = (X - mean) / standard deviation
where X is the score we are interested in.
z-score = (500 - 694) / 112
z-score ≈ -1.732
Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.
So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.
(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.
z-score = (X - mean) / standard deviation
where X is the score we are interested in.
z-score = (900 - 694) / 112
z-score ≈ 1.839
Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.
So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.
(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.
We use the z-score formula to find the z-score corresponding to the 99th percentile:
z-score = invNorm(0.99)
z-score ≈ 2.326
Now, we use the z-score to find the score corresponding to the 99th percentile:
X = mean + (z-score * standard deviation)
X = 694 + (2.326 * 112)
X ≈ 694 + 260.512
X ≈ 954.512
So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.
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An equation is shown:
−np − 4 = 2(c − 3)
Which of the following solves for n?
n = the quantity 2 times c plus 2 all over negative p
n = the quantity 2 times c plus 10 all over negative p
n = the quantity 2 times c minus 2 all over p
n = the quantity 2 times c minus 10 all over p
The solution of given equation for n would be n = (2c - 2)/(-p)
In this question, we have been given an equation.
We solve given equation for n.
−np − 4 = 2(c − 3)
−np − 4 + 4 = 2(c − 3) + 4
−np= 2c - 6 + 4
-np = 2c - 2
np = -2c + 2
np * 1/p = (-2c + 2) * (1/p)
n = (-2c + 2)/p
n = (2c - 2)/(-p)
Therefore, the solution of given equation for n would be n = (2c - 2)/(-p)
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Answer:
The answer would be n = (2c - 2)/(-p)
Step-by-step explanation:
Hope this helps! :D
Write 5/3 as a mixed number.
Answer:
Step-by-step explanation:
the answer would be 1 and 2/3
3 goes into 5 one time and you have 2 left
Which best describes the range of the function f x 2 3 x?.
The range of the function f(x) = 2(3)x is best described by y > 0. Particularly the function when the constant is e, a function whose value is a constant raised to the power of the argument.
What is range of function?The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response. The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
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PQR is an isosceles triangle in which PQ= PR Mand N are points on PQ and PR such that angle MRQ= angle NQR. Prove that triangles QNR and RMQ are congruent.
We have proved that triangles QNR and RMQ are congruent.
What is an isosceles triangle?
An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.
∠MRQ ≅ ∠NQR . . . . given
QR ≅ RQ . . . . reflexive property
∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR
ΔQNR ≅ Δ RMQ . . . . ASA postulate
Hence, we have proved that triangles QNR and RMQ are congruent.
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If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.
A. 12X
B. X-14
C. X-13
D. X-12
Answer:
Step-by-step explanation:
what is the t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14? r lab
The appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
Given:
The t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14.
It is the 97.5%-quantile of the t-distribution with 14 degrees of freedom.
In the figure the dashed line shows the value such that the yellow shaded area has size 0.975: the 97.5%-quantile is the value such that 97.5% of the probability mass is to the left of it and the rest to the right.
so t - multiplier = 2.15.
Therefore the appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
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The legs of an isosceles triangle are 0.3 foot less than twice the base. The perimeter of the triangle is 4.9 feet.
What is the length of one of the triangle’s legs?
A. 1.1 feet
B. 1.4 feet
C. 1.9 feet
D. 2.2 feet
Answer:
it's D of the triangles legs this is the answer
Given that sec(θ) = 8 and tan(θ) < 0, find the following:
cos(θ) =
sin(θ) =
tan(θ) =
csc(θ) =
cot(θ) =
Rationalize denominators and tell which ones are negative.
The value cos(θ), sin(θ), tan(θ), csc(θ) and cot(θ) are 1/8, (-3√7)/8, -3√7, -(8√7)/21 and -√7/21 respectively
How to find the trigonometric ratio of the angle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Given that: sec(θ) = 8 and tan(θ) < 0. This implies:
cos (θ) = 1/8 and tan(θ) is negative. This means θ is quadrant 4
(Note: cos (θ) = 1/sec(θ) )
Using the given information, we can sketch the location of the angle θ in the quadrant (See the attached image).
Thus, we can calculate the value of side d using the Pythagoras theorem
d = √(8² - 1²) = √63 = 3√7
The side is -d = -3√7
Note: the side d is negative in the quadrant
Therefore:
cos(θ) = 1/sec(θ) = 1/8
sin(θ) = (-3√7)/8
tan(θ) = (-3√7)/1 = -3√7
csc(θ) = 8/(-3√7) = - (8√7)/21
cot(θ) = -1/(-3√7) = -√7/21
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A right triangle has coordinates (-3, 4), (3,6), and (-1,-2). What is the area of the right triangle?
help
Answer:
2728
Step-by-step explanation:
Answer:
20 sq units
Step-by-step explanation:
A quick sketch graph will show the right angle is at (-3 ,4)
The lengths of the shorter sides are both sqrt(2^2 + 6^2) = sqrt(40)
Area = 1/2 x (sqrt(40))^2 = 20
If you didn’t have a right angle you could find the lengths of all sides a, b and c
Calculate the semi perimeter s = (a+b+c) / 2
And the area = sqrt(s(s-a)(s-b)(s-c))
Try and use this method to check the first one
A bank machine uses pin numbers of 4 digits. The of odd pin numbers is:
Answer:15
Step-by-step explanation:hope this helps
A 16-ounce bottle of water from Store A costs $1.28. The cost in dollars, y, of a bottle of water from Store B is represented by the equation y=0.07x, where x is the number of ounces. What is the cost per ounce of water at each store? Which store's bottle of water costs less per ounce?
The cost of per ounce of water at store A is $0.08 and at store B is $0.07 , the water in the store B will cost less per ounce .
In the question ,
it is given that
in store A the cost of 16 ounce of water is $1.28 ,
so the cost of 1 ounce of water in store A is = 1.28/16
= $0.08
in store B the cost of water is represented by the equation
y = 0.07x
where "x" is the number of ounces of water ,
which means
the cost of 1 ounce of water in store B is = $0.07
hence , the water in store B will cost less .
Therefore , The cost of per ounce of water at store A is $0.08 and at store B is $0.07 , the water in the store B will cost less per ounce .
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2- Which equations have no solution? Select all
that apply.
x + 3 = 2x + 3
8 = 2(x+4) − 2x.
5x-2x = -7x+1
2x-3 = 5x - 3-3x
4xx+6= 2(x+1)+x
Answer: E has no solution
Step-by-step explanation: It is a contradiction
keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses? What linear equation in STANDARD FORM can she use to model the situration?
Cheddar Cheese: $3/lb
Swiss Cheese: $5/lb
Answer:
Only cheddar 10 pounds
Only swiss 6 pounds
Use the equation to find out different combinations.
3x + 5y = 30
For example, 1 pound of cheddar and 5.4 pounds of swiss.
Step-by-step explanation:
Let x = cheddar
Let y = swiss
3x + 5y = 30
If we only wanted cheddar let y be 0
3x =30 Divide both sides by 3
x = 10
You can buy 10 pounds of cheddar.
If we only wanted swiss let x be 0
5y = 30 Divide both sides by 5
y = 6
You can buy 6 pounds of swiss.
1 pound of cheddar:
3(1) + 5y = 30 Subtract 3 from both sides
5y = 27 Divide both sides by 5
y = 5.4
URGENT: If a pack of five compasses sells for $3.95,
How much does one compass cost?
Answer:
0.79 dollars
Step-by-step explanation:
Divide 3.95 by five to find the cost of one compass.
suppose you have 6 pairs of sock in your sock drawer and every pair has a unique color. it is still dark out in the morning when you get dressed, so you just pull socks out of the drawer at random, one at a time, until you have removed two matching socks. what is the probability that you pull out exactly 5 socks from your sock drawer in the morning before you get a matching pair of socks?
The probability there is at least one pair is therefore 1−p.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
It is little known, but socks have individual identities. There are (166) equally likely ways to choose 6 socks from the 16.Now we find the number of ways to choose 6 socks, so that there is no pair among them. There are (86) ways to choose the "types" of sock we will have. For each choice of 6 types, there are 26 ways to choose the actual socks. For at each chosen "type" of sock, we have 2 choices as to which of the two socks of that type to take.hence,The probability there is at least one pair is therefore 1−p.
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Find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
To find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
Area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
A triangle's feature known as SAS, or "Side, Angle, Side," has two sides and an angle that are both known.
The space occupied between the sides of the SAS triangle in a plane can thus be calculated with the use of the SAS triangle area formula.
The formula to find area of SAS triangle is:
Area = ½ ab Sin C = ½ × 29 × 36 × sin 62
Thus, Area = 522 × sin 62 = 522 × 0.88 = 459.36
Hence the answer is, Area of SAS triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
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Write an equation in slope-intercept form of the line with the given
characteristics.
slope = 2/5
; passes through (–3, 1)
Answer:
The equation of the line in slope-intercept form is [tex]y=0.4x+2.2[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form can be calculated as follows ?
The first step is to find the slope-intercept form of the given line by the point-slope form formula as follows
[tex]y-y_{1}=m(x-x_{1})[/tex]
Where [tex]m[/tex] is the slope of the line
Write the given value of the slope
[tex]m=\frac{2}{5}[/tex]
Convert the value of the slope into decimal
[tex]m=0.4[/tex]
The second step is to substitute [tex]0.4[/tex] for [tex]m[/tex], [tex]1[/tex] for [tex]y_{1}[/tex], [tex]-3[/tex] for [tex]x_{1}[/tex] in the point-slope form formula
[tex]y-1=0.4(x-(-3))[/tex]
Take out the inner bracket on the right side of the equation
[tex]y-1=0.4(x+3)[/tex]
Expand the right side of the equation
[tex]y-1=0.4x+1.2[/tex]
Add [tex]1[/tex] to both sides of the equation
[tex]y-1+1=0.4x+1.2+1[/tex]
Simplify the equation
[tex]y=0.4x+2.2[/tex]
Hence the equation of the line in slope-intercept form is
[tex]y=0.4x+2.2[/tex]
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fat content in 10 hotdogs is measured as: 25.2, 21.3, 22.8, 17, 29.8, 21, 25.5, 16, 20.9, 19.5. find a 95% prediction interval that bounds the fat content of the next hot dog.
Statistics with a 95% prediction interval that indicate how much fat the next hot dog will contain 21.83±2.917
Take into account the following sample of n = 10 randomly chosen hot dogs' fat content (in percentage):
A 95% CI for (interval estimate of) the population, given that these were chosen from a normal population distribution
x±[tex]t_{0.025,9} * s/\sqrt{n}[/tex]
= 21.83± 2.262 * 4.079/[tex]\sqrt{10}[/tex]
= 21.83±2.917
But let's say you want to know how much fat will be in a single of this kind of hot dog before you consume it. Just x 21.90 makes a point prediction, which is comparable to a point estimate. Unfortunately, the statistical prediction provides no details regarding accuracy or dependability.
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What is the 2s fact?.
The value of 2 factorial would be 2.
What is a factorial of a number?
Factorial is the product of all positive integers less than or equal to a given positive integer, denoted by that integer, and an exclamation point in mathematics. Thus, factorial seven is written 7! which means 1*2*3*4*5*6*7. Factorial zero is defined as one.
As the definition says that the factorial is the product of all the positive integers less than or equal to the given number till one.
We have to find the value of 2 factorial.
2! = 2 * 1
= 2
Hence, the value of 2 factorial would be 2.
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Charlotte is making 6 pounds of trail mix using raisins and 3 different types of nuts.
The table shows the amounts of different types of nuts that she has.
Type of Nut Amount (in pounds)
almonds
7
8
cashews
1
1
2
peanuts
2
3
8
pecans
1
1
4
walnuts
1
3
4
Charlotte uses all of the almonds, cashews, and peanuts that she has.
Which of the following explains how she can find the exact amount of raisins she needs?
A.
Round
7
8
pound to 1 pound,
1
1
2
pounds to 2 pounds, and
2
3
8
pounds to 2 pounds.
Then add the rounded amounds and subtract that total from 6 pounds.
B.
Add
7
8
pound,
1
1
2
pounds,
2
3
8
pounds,
1
1
4
pounds, and
1
3
4
pounds.
Then subtract 6 pounds from that total.
Answer:
It Should be B because You need to add all of the pounds and subtract it by six
Step-by-step explanation:
The Grade 8 students had an
end-of-the-year dance.
The disc jockey charged $85 for setting
up the equipment, plus $2 for each
student who attended the dance.
The disc jockey was paid $197.
How many students attended the dance?
a) Write an equation you can use to
solve the problem.
b) Solve the equation.
c) Check your answer and explain
how you know it is correct.
Answer:
1. You can use the equation 2x + 85 = 197
2. 2x+ 85 =197
-85 -85
-------------------------
2x = 112
/2 /2
------------------------
x = 60
x is the number of students that went to the dance
plug in 60 into x in the equation I gave to check
Y=4/5x-5
Slope:
Y-intercept:
tiffany walks x miles in 90 minutes. How many miles can she walk in 120 minutes?
A. 4/3 x
B. 30x
C. 3/4
D. 0.75x
Answer: A. 4/3 x
Step-by-step explanation:
x miles in 90 minutes to ? miles in 120 minutes
90 miles to 120 miles is 1.3333 which is equal to 4/3.
Multiply it to x and you have A. 4/3x
you have 3 bags of candy each with 4 pieces of candy in them. How many pieces of candy do you have?
Answer:
12
Step-by-step explanation:
3x4
You need 2yds of fabric for 3 pillows. And 6yds to cover 9 pillows how much fabric to cover 15 pillows
With respect to the pattern, 10yds of fabric will be required to cover 15 pillows.
Define pattern in mathematics.
A series of identical objects, forms, or numbers is referred to as a pattern in mathematics. Every type of event or thing has a pattern that we can associate with it. An object's membership in a pattern is determined by a rule, which identifies which items do and do not fit the bill.
Solution Explained:
As seen from the question, the patterns are increasing by 4 and 6.
PATTERN 1: 2, 6, 10...
PATTERN 2: 3, 9, 15...
Hence, the next number is 10. So, 10yds of fabric will be required to cover 15 pillows.
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Find the value of the specified trig ratio. Be sure to reduce when possible.
The value of cosC is 8/17.
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
In the figure,
Adjacent=CB=16
hypotenuse=AC=34
The formula for the cos function:
cos[tex]\theta[/tex]=adjacent/hypotenuse
cosC=16/34
divide 16 and 34 by 2 to simplify further
cosC=8/17
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Answer the question below. Type your response in the
space provided.
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