Answer:
$15.54
Step-by-step explanation:
IF EACH STUDENT GETS 1 PENCIL, AND $0.74X21=$15.54 THEN THAT IS THE TOTAL COST
The pencils cost $15.54 in all.
Hope I helped!
Find point C on the x-axis so that AC+BC is a minimum.
A(−1,7), B(5,−4)Write a rule for the translation of △LMN to △L′M′N′.
Answer:
The coordinate of the point C is (-10/3, 0)
Step-by-step explanation:
The coordinates of the given points are A(-1, 7), B(5, -4)
Let the coordinate of the point C on the x-axis = C(x, 0)
Therefore, we have;
The square of the distance, d², between two points having coordinates, (x₁, y₁), and (x₂, y₂), is given by the following formula;
d² = (x₂ - x₁)² + (y₂ - y₁)²
The square of the distance from the point C to A, AC², is given as follows;
AC² = (x - (-1))² + (0 - 7)² = (x + 1)² + 7² = x² + 2·x + 1 + 49 = x² + 2·x + 50
Similarly, the square of the distance from the point C to B, AB², is given as follows;
BC² = (x - (-4))² + (0 - 5)² = (x + 4)² + 5² = x² + 10·x + 25 + 25= x² + 10·x + 50
Therefore;
AC² + BC² = x² + 2·x + 50 + x² + 10·x + 50 = 2·x² + 12·x + 100
(AC + BC)² = AC² + BC² + 2·AB·BC
2·AB·BC = √(4·AB²·BC²) =√(4 × (x² + 2·x + 50) × (x² + 10·x + 50))
2·AB·BC = √(4·x⁴ + 48·x³ + 480·x² + 2400·x + 10,000)
(AC + BC)² = 2·x² + 12·x + 100 + √(4·x⁴ + 48·x³ + 480·x² + 2400·x + 10,000)
AB + BC will be smallest when (AC + BC)² is smallest
Differentiating (AC + BC)² and equating to zero, to find the minimum point, gives;
d(2·x² + 12·x + 100 + √(4·x⁴ + 48·x³ + 480·x² + 2400·x + 10,000))/dx = \(\dfrac{16\cdot x^{3} + 144\cdot x^{2} + 960\cdot x + 2400}{2\cdot \sqrt{4\cdot x^{4} + 48\cdot x^{3} + 480\cdot x^{2} + 2400\cdot x + 10000}} + 4\cdot x +12 = 0\)
Solving using an online application, gives x = -10/3
Therefore, the point C has coordinates C(-10/3, 0).
PLS HELPP I NEED AN ANSWER ASAP ILL GIVE BEAINLIEST
The top right graph could show the arrow's height above the ground over time.
Which graph models the situation?The initial and the final height are both at eye level, which is the reference height, that is, a height of zero.
This means that the beginning and at the end of the graph, it is touching the x-axis, hence either the top right or bottom left graphs are correct.
The trajectory of the arrow is in the format of a concave down parabola, hitting it's maximum height and then coming back down to eye leve.
Hence the top right graph could show the arrow's height above the ground over time.
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Given g(x) = 3x+3, find g(6)
Answer:
g(6)=21
Step-by-step explanation:
Given g(x)= 3x+3, Find g(6)
1. Replace g(x) with g(6), and x with 6. The equation will now look like this: g(6)=3(6)+3
2. Multiply 3 and 6, to equal 18. The equation will now look like this: g(6)=18+3
3. Add 18 and 3 to equal 21. The Answer is g(6)=21
WILL GIVE BRAINLIEST
A pair of sunglasses is discounted by 30%. The discounted price is $35. What was the original price of the sunglasses?
(Please show work!)
help me please help urgent
Answer:
8°
Step-by-step explanation:
For exterior angle QRS, angles RPQ and PQR are its remote interior angles.
m<QRS = m<RPQ + m<PQR
4x - 15 = x + 1 + x - 2
2x = 14
x = 7
m<RPQ = x + 1 = 7 + 1 = 8
You have 0.895 m of ribbon to hang the “Grand Opening” sign. You need 100 cm to hang it correctly. Do you have enough ribbon? If not,how much more do you need?
Answer:
no you need 10.5cm
Step-by-step explanation:
so convert 0.895m to cm by multiplying it by 100 to get 89.5 which is less
so take the required 100-89.5
Subtraction is a mathematical operation. The ribbon is not enough. 10.5 cm of ribbon is more needed.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
It is known that 1 meter is equal to 100cm, therefore, the length of the ribbon will be equal to,
\(\rm 1\ m =100\ cm\\\\0.895\ m = 0.895 \times 100 = 89.5\ cm\)
Now, as the ribbon needed is 100 cm, therefore, the length of ribbon that is needed more is
\(\rm \text{length of the ribbon needed} = 100\ cm - 89.5\ cm = 10.5\ cm\)
No, the ribbon is not enough. 10.5 cm of ribbon is more needed.
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helpppp me asap i hate theseeee
Answer:I think CBD
Step-by-step explanation:
A dataset on 91 roller coasters lists the Duration of the ride in seconds in addition to the Drop height in feet for some of the coasters. One coaster, the "Tower of Terror," is unusual for having a large drop but a short ride. After setting it aside, a regression to predict Duration from Drop for the remaining 90 coasters has R^2 = 29.4%. Complete parts a through c a) What are the variable and units in this regression? The predictor variable is ____ in units of _____and the response variable is _____ in units of ____
b) What units does the slope have? - Feet per second - Feet - Seconds - Seconds per foot c) Is the slope probably positive or probably negative? Explain The slope is probably _____ because ______
a) The predictor variable is Drop in units of feet and the response variable is duration in units of seconds.
b) The units of the slope is seconds per foot.
c) The slope is probably negative because a taller drop height typically leads to a longer ride duration.
a) The predictor variable in this regression is Drop, which represents the drop height in feet of the roller coasters, and its units are feet. The response variable is Duration, which represents the duration of the ride in seconds, and its units are seconds.
b) The units of the slope in this regression are seconds per foot. This means that for every one unit increase in the drop height in feet, the duration of the ride increases or decreases by the value of the slope, measured in seconds per foot.
c) The slope is probably negative because a taller drop height typically leads to a longer ride duration, and the Tower of Terror coaster, with its unusually short duration despite a large drop height, has been removed from the analysis.
Therefore, the remaining 90 coasters in the dataset would likely exhibit a negative relationship between drop height and duration, meaning that as the drop height increases, the duration of the ride decreases.
The low R-squared value of 29.4% suggests that there is a lot of variability in the relationship between drop height and ride duration among the roller coasters in the dataset, but the negative slope indicates a generally decreasing trend.
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For the function f (x) = 5 - 7x, find the difference quotient .
When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are:
When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are statistically significant.
In statistical analysis, we use hypothesis testing to determine whether the results of a sample are likely to be representative of the population as a whole. If the results are statistically significant, we can infer that there is a low probability that the observed differences between the sample and the population occurred by chance alone.
This allows us to generalize the findings from the sample to the larger population with a reasonable degree of confidence.
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A store marks up a laptop 150% from its original price of $399. There is a sale for 25% off all items in the store. What is the sale price for the computer
Answer:
multiply the original price ($299) by the first markup percentage (150%)
299*1.50= $448.50
that is markup price!
then you have to do the sale % (25%)
so you'll multiply your (25%) by your new price ($448.50)
448.50*.25= $112. 125
then you will subtract the sale price ($112.125) by the upcharged price ($448.50)
448.50-112.125= 336. 375
= $336. 38(round off)
Old Man Withers just died. He left his collection of baseball cards to his two sons. Bill got 55% of the collection and his brother Bob received the rest.
How many cards did Bill receive if Bob received
360 cards, then how many cards did Bill as inheritance from his father?
Answer:
Step-by-step explanation:
Bill = 55% of the entire collection
Bob = 45% of the entire collection (Since we know 100 - 55 = 45)
We are also told that Bob received 360 cards.
This means that 45% = 360 cards.
First step is to find how many cards is 1%. To do this, divide 360 by 45.
1% of entire collection = \(\frac{360}{45} = 8\) cards
This means that since Bill gets 55% of the entire collection, you multiply 8 by 55.
Bill = 8 x 55 = 440 cards.
Answer:
440
Step-by-step explanation:
If f(x) is an exponential functionwhere f(-1) = 26 andf(6.5) = 14, then find the value off(5), to the nearest hundredth.
The general form of an exponential function is:
\(y=a\cdot b^x^{}\)where a ≠ 0, b > 0 and b ≠ 1
f(-1) = 26 and f(6.5) = 14, that is,
\(\begin{gathered} 26=a\cdot b^{-1} \\ 26=\frac{a}{b} \\ 26\cdot b=a \end{gathered}\)\(\begin{gathered} 14=a\cdot b^{6.5} \\ 14=26\cdot b\cdot b^{6.5} \\ 14=26\cdot b^{7.5} \\ \frac{14}{26}=b^{7.5} \\ \ln (\frac{14}{26})=7.5\cdot\ln b \\ -\frac{0.619}{7.5}=\ln b \\ e^{-0.0825}=b \\ 0.92=b \end{gathered}\)Then,
\(\begin{gathered} a=26\cdot b \\ a=26\cdot0.92 \\ a=23.92 \end{gathered}\)Finally, the function is:
\(y=23.92\cdot0.92^x^{}\)if+the+correlation+between+two+variables+is+.496,+how+much+of+the+variance+has+not+been+accounted+for?++a.+24.6%++b.+49.6%++c.+50.4%++d.+75.4%
The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.
If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.
A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.
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Order the following expressions by their values from least to greatest.
-2 a+c b
The expressions ordered from least to greatest are: -2 < b < (a + c)
What is expression?In maths, an expressiοn is a cοmbinatiοn οf numbers, variables, functiοns (such as additiοn, subtractiοn, multiplicatiοn οr divisiοn etc.)
Expressiοns can be thοught οf as similar tο phrases. In language, a phrase οn its οwn may include an actiοn, but it dοesn't make a cοmplete sentence.
According to the question:
-1 < a < 0
2 < b < 3
4 < c < 5
Now, we have the expression a + c
= (-1 < a < 0) + (4 < c < 5)
= (-1 + 4) < (a + c) < (0 + 5)
= 3 < (a + c) < 5
Thus, we have the expressions ordered from least to greatest are:
-2 < 2 < b < 3 < (a + c) < 5
-2 < b < (a + c)
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Complete question:
Find the area of the surface cut from the paraboloid x^2 + y^2 - z = 0 by the plane z = 20. The surface area is. (Type an exact answer in terms of pi.)
The area of the surface cut from the paraboloid x^2 + y^2 - z = 0 by the plane z = 20 is 80π√5 square units.
For the area of the surface cut from the paraboloid x^2 + y^2 - z = 0 by the plane z = 20, we need to calculate the surface area of the intersection curve.
The intersection curve is obtained by setting z = 20 in the equation of the paraboloid:
x^2 + y^2 - 20 = 0
This equation represents a circle with radius √20 = 2√5 centered at the origin (0, 0). The equation can be written in polar coordinates as r = 2√5.
To find the surface area of the circle, we can use the formula for the circumference of a circle and multiply it by the height of the cylinder formed by the circle when revolving around the z-axis.
The circumference of the circle is 2πr, where r = 2√5. So the circumference is 4π√5.
The height of the cylinder formed by the circle is the difference between the maximum and minimum z-values, which is 20 - 0 = 20.
Therefore, the surface area of the intersection curve is given by:
Surface Area = Circumference × Height
= 4π√5 × 20
= 80π√5
So, the area of the surface cut from the paraboloid is 80π√5 square units.
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what is the mass of an object that weighs 7 kg and 50 N?
Answer:
7kg
Step-by-step explanation:
mass: amount of matter in a substance,
SI Unit: kg
It has nothing to do with N (weight) in this case so take the kg value as the mass
Answer:
0.71 kg
Step-by-step explanation:
a common equation in physics is w = mg
we can rearrange this to m = w/g
g is the acceleration of gravity: 9.81 m/s^2
w is the weight of the given equation of the object: 7 kg
so m = 7 kg ÷ 9.81 m/s^2
this gives us: m = 0.71 kg
What is 5x-2+7x-5 simplified?
Answer:
12x -7
Step-by-step explanation:
Sally has a budget for school stationery of $37, but has already spent $22.72 on books and folders. Let p represent the amount that Sally can spend on other stationery. Write an inequality that shows how much she can spend on other stationery, and solve for p.
Answer:
\(p\le 14.28\)
Step-by-step explanation:
Total budget for school stationery = $37
She has already spent $22.72 on books and folders.
Left amount = $37 - $22.72
= $14.28
Let p represent the amount that Sally can spend on other stationery. It implies that "p" must be less than or equal to $14.28 .
Hence, the required inequality is :
\(p\le 14.28\)
In a binomial situation, n=18 and π=0.60. Determine the expected
value
The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.
In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.
In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.
n = 18 (number of trials)
π = 0.60 (probability of success for each trial)
To find the expected value:
E(X) = np
Substitute the given values:
E(X) = 18 * 0.60
Calculate the expected value:
E(X) = 10.8
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Find x:
(Round the answer to the nearest tenth if there is a decimal)
Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)
Use tangent:
tan x = 8/15
x = arctan (8/15)
x = 28.1° (rounded)
Step-by-step explanation:
help this is my homework question and i don’t understand it
A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 150 What is the theoretical probability of 5
students from your school being selected as contestants out of 8 possible contestard spots?
P(5 students selected)
(Type an integer or decimal rounded to three decimal places as needed)
Cus
The theoretical probability of randomly selecting 5 students from my schools is 0.00000001237
probability of an eventprobability = required outcome / total possible outcomes
Required outcome = 5 students from the 40. Here , we have
40C5 = 65008
Total possible outcomes = 8 students From the total contestants . Here , we have
150C8 = 5257211409450
Hence, selecting 5 students from my school :
P(5 from my school) = 65008/5257211409450
P(5 from my school ) = 0.00000001237
Hence, the theoretical probability is 0.00000001237
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4. a picture can be added to a text in nine different locations on a page. if four different pictures are to be placed in the text, how many different designs are there?
As per the combination method, there are 3,024 different designs that can be created with four different pictures placed in nine different locations on a page.
There are seven options for the third picture and six options for the fourth picture.
To determine the total number of designs, we can use the multiplication principle, which states that the number of ways two or more independent events can occur together is equal to the product of the number of ways each event can occur individually.
Therefore, the total number of designs that can be created by placing four different pictures in nine different locations on a page can be found by multiplying the number of options for each picture:
9 x 8 x 7 x 6 = 3,024
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I can't figure out this equation. Can someone help me?
4x−7= 8x + 33
Answer:
x = -10
Step-by-step explanation:
Subtract 4x on both sides
4x-7 = 8x+33
(4x-7)-4x = (8x+33)-4x
-7 = 4x+33
Subtract 33 on both sides
-7 = 4x+33
-7-33 = (4x+33)-33
-40 = 4x
Divide both sides by 4
-40 = 4x
-40/4 = 4x/4
-10 = x
Therefore, x=-10
Step-by-step explanation:
4x-7=8x+33
-7-33=8x-4x
-40= 4x
Divide both sides by 4
-10=x
therefore x=-10
-10
ious Activity
Type har
-5
10+y
O
-10
-20
5
Select the quadratic inequality that represen
graph.
Ov²(x+3)²-24
vs-(x-3)²+24
v2 - (x-3)2+24
Oys (x+3)²-24
O
The quadratic inequality defined on the graph is given as follows:
y ≥ 2/3(x + 3)² - 24.
How to define the quadratic inequality?The coordinates of the vertex of the quadratic function are given as follows:
(-3, -24).
Hence the quadratic function is given as follows:
y = a(x + 3)² - 24.
In which a is the leading coefficient.
When x = 3, y = 0, hence the leading coefficient a is obtained as follows:
0 = a(3 + 3)² - 24
36a = 24
a = 24/36
a = 2/3.
Hence:
y = 2/3(x + 3)² - 24.
The quadratic function has a solid curve, and the values above it are pained, hence the inequality is given as follows:
y ≥ 2/3(x + 3)² - 24.
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prove that triangle fgh ≅ triangle Ijh
options for 1: Given, Vertical angles are congruent, or linear pair angles are supplementary.
options for 3: same as 1
options for 4: angle-angle- side, Angle-side - angle, Side-angle-side, or SSS
Answer:
Statements and Proofs
1) m∠G= m∠J=39° | Given
2) FG=IJ=6 | Given
3) ∠GHF≅∠JHI | Vertical angles are congruent.
4) △FGH≅△IJH | Angle-angle-side congruence
I hope this works! Thanks and have a great day!
The triangle FGH ≅ triangle IJH using angle angle side congruency.
In the figure of the triangles FGH and IJH,
Measure of angle G = 39 degree
Measure of angle J = 39 degree
⇒ m ∠G ≅ m ∠J
Measure of side FG = 6 units
measure of IJ = 6 units
⇒FG ≅ IJ
Measure of ∠GHF ≅Measure of ∠IHJ as both are vertically opposite angles.
By applying Angle Angle side congruency,
ΔFGH ≅ΔIJH
Therefore, the triangle FGH and IJH are congruent to each other using Angle Angle side congruency.
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Sara drives 96 miles on 3.2 gallons of gas. She uses this information to calculate how many m
Using this result, how many miles can Sara drive on 12.5 gallons of gas?
O 37.5
O2.4
O 375
O 240
How to form a polynomial with given zeros and degree?
To form a polynomial with given zeros and degree, we need to use the fact that if a polynomial has a zero of x = a, then it can be factored as (x - a) times some other polynomial.
This means that if we know the zeros of a polynomial, we can write it in factored form, and then multiply out the factors to get the polynomial in standard form.
The degree of the polynomial tells us how many factors are necessary. For example, if the degree is 3, we know that the polynomial can be factored into three linear factors, one for each zero.
To illustrate this process, let's say we want to form a polynomial of degree 4 with zeros of x = 2, x = -1, and x = 3. We would start by writing the polynomial in factored form as:
f(x) = (x - 2)(x + 1)(x - 3)(ax + b)
Since the degree is 4, we need to include one more factor. We can use the coefficients a and b to determine this factor. To do so, we can either use the value of the leading coefficient (which is a in this case) or a point on the polynomial (i.e., a value of x and f(x)).
Once we have determined the value of a, we can solve for b by setting a point on the polynomial equal to a known value.
Finally, we can multiply out the factors to get the polynomial in standard form:
f(x) = (x - 2)(x + 1)(x - 3)(2x - 4)
f(x) = 2x^4 - 8x^3 - 13x^2 + 22x - 12
In conclusion, to form a polynomial with given zeros and degree, we need to use the fact that a polynomial can be factored as (x - a) times some other polynomial if it has a zero of x = a.
We can write the polynomial in factored form, determine the missing factor(s) using the degree and coefficients, and then multiply out the factors to get the polynomial in standard form.
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ASAP please help meeeeeeeeeee
Answer:
Step-by-step explanation:
1/16 + 1/2 = 1/16 + 8/16 = 9/16