Answer:
Step-by-step explanation:
From the symmetry in the table, we can see that the vertex of the parabola is located at (-5, -2). We will pick another point from the table to use in our model to solve for the a value, just in case there is one. I picked (-4, -1). Any point from the table will work.
Our model is
[tex]y=a(x-h)^2+k[/tex] where h and k are the coordinates of the vertex and x and y are the coordinates from the other point chosen from the table. Filling in to solve for a:
[tex]-1=a(-4+5)^2-2[/tex] and
[tex]-1=a(1)^2-2[/tex] and
-1 = a - 2 so
a = 1.
Now we can fill in the equation with the coordinates of the vertex and the value found for a to get
[tex]y=(x+5)^2-2[/tex] You don't need to put the 1 out in front; it's unnecessary. Your choice is the last one there in the list.
There is a mound of g
pounds of gravel in a quarry. Throughout the day, 200
pounds of gravel is added to the mound. Two orders of 700
pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,000
pounds of gravel.
Answer:
2400
Step-by-step explanation:
before anything got taken away they added 200 wich means before they added that they had 2200 and if 700 pounds were removed twice that would mean the mound lost 1400 pounds and so if you add 1000 to the 1400 that they took you can find the amount that was there before.l
Describe a situation that could be represented by the expression `4-2.27`.
Answer:
I had 4 dollars, but I spent 2.27 on my new pencil.
Step-by-step explanation:
You need to create a situation where you have 4 of 'blank' and you take away 2.27 of 'blank' to answer this question.
Find the equation of the line that passes through the given points. (Use x as your variable.) (0,5),(6,0)
Answer:
y = - [tex]\frac{5}{6}[/tex] x + 5
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5 ) and (x₂, y₂ ) = (6, 0 )
m = [tex]\frac{0-5}{6-0}[/tex] = [tex]\frac{-5}{6}[/tex] = - [tex]\frac{5}{6}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = - [tex]\frac{5}{6}[/tex] x + 5 ← equation of line
The weight of Amara to the weight of toyin is 3:5, if Amara weighs 30 kg , how many more does Toyin weight?
Write 4 to the 3ed power using repeated multiplication. Then find the value of 4 to the 3ed power
Answer:
4x4x4 and the value of 4^3=64
Step-by-step explanation:
4x4x4 is equivalent to 4^3. This is because using exponents mean multiplying the base number by itself by 2 if the exponent is 2, if it was 3 then you would multiply 4 by itself three times.
I will mark you brainiest!
Which quadrilaterals have all of the properties of a parallelogram?
A) rhombus,kite, and trapezoid
B) rhombus, rectangle, and square
C) rhombus, kite, and square
D) Rhombus trapezoid, and rectangle
Answer:
The correct answer is B) rhombus, rectangle, and square.
A parallelogram is defined as a quadrilateral with two pairs of parallel sides. A rhombus, a rectangle, and a square are all special cases of parallelograms with additional properties.
A rhombus is a parallelogram with all sides equal in length.
A rectangle is a parallelogram with four right angles.
A square is a parallelogram with four equal sides and four right angles.
A kite and a trapezoid are not parallelograms since they do not have two pairs of parallel sides. While a trapezoid has one pair of parallel sides, a kite has no parallel sides.
Find the value of p in this proportion show work below answer here P=
The value οf p that satisfies the prοpοrtiοn is 16.
What is a prοpοrtiοn in math?Prοpοrtiοn is explained majοrly based οn ratiο and fractiοns. A fractiοn, represented in the fοrm οf a/b, while ratiο a:b, then a prοpοrtiοn states that twο ratiοs are equal. Here, a and b are any twο integers. The ratiο and prοpοrtiοn are key fοundatiοns tο understand the variοus cοncepts in mathematics as well as in science.
Prοpοrtiοn finds applicatiοn in sοlving many daily life prοblems such as in business while dealing with transactiοns οr while cοοking, etc. It establishes a relatiοn between twο οr mοre quantities and thus helps in their cοmparisοn.
Tο sοlve fοr p in the prοpοrtiοn:
10/p = 5/8
We can crοss-multiply tο οbtain:
5p = 80
Dividing bοth sides by 5, we get:
p = 16
Therefοre, the value οf p that satisfies the prοpοrtiοn is 16.
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The Ministry of Transport and Mining hired a firm to conduct a traffic study before expanding the city streets. Two companies submitted bids for the job. The ministry hired the second company (company B) because they had more experience and offered a better rate. They studied the movement of the traffic on a specific roadway. The first day of the study was the second Monday in September. They found that 12,665 cars, 23,709 small commercial vehicles, 1,024 medium trucks, 7,096 lange macks, and 660 other vehicles used the roadway during the evaluation period.
0f the vehicles classified as "other vehicles," 213 of them are morcycles How many of the other vehicles were not motorcycles?
Answer: i got 213
Step-by-step explanation:
If she makes her goal pace 80% of the time and plans to run for the next 10 days how likely will she make her goal pace
every day
If she makes her goal pace 80% of the time and plans to run for the next 10 days, the probability or likelihood that she will make her goal pace every day is 80%.
What is probability?Probability describes the chance, odds, or likelihood of an expected outcome, event, or success occurring when there are many possible outcomes.
Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.
Thus, it is 80% likely that she will make her goal pace every day if she runs for the next 10 days.
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I neeedddd helppppp???
Answer:
(-2,-4)
Step-by-step explanation:
The solution to a system of equations is the point at which the lines (that are defined by the equations) intersect, or touch each other.
In the graph, we can see that the lines intersect when x = -2 and y = -4.
In the format (x,y), this is expressed as: (-2,-4)
The points C(-8, -9), D(-2,-2), E(0, 7), and F(-6, 0) form rhombus CDEF.
Plot the points then click the "Graph Quadrilateral" button. Then find the area of the
rhombus.
Answer:
The area of the rhombus CDEF is 32 units squared.
Step-by-step explanation:
The area of the rhombus CDEF is 24 square units. This can be determined by using the formula for finding the area of a rhombus which is A = 1/2 × d1 × d2 where d1 and d2 are the lengths of the diagonals of the rhombus. In this case, d1 is the distance from C to E and d2 is the distance from D to F. Calculating the lengths of the diagonals gives d1 = 8.9 and d2 = 8. Therefore, the area of the rhombus is 24 square units.
STATISTICS MATH. SOMEONE PLEASE HELP WITH THIS!! ILL GIVE YOU BRAINLIST ANSWER. IMAGE ABOVE
Answer:
u rock tgu hjgr yyihh yihgg
Please help me with this math!
Pythagorean theorem: This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.
12² + 12² = x²
288= x²
x =16.98 = 17
(x² + 3x + 2) ÷ (x + 2)
Answer:
x+1
Step-by-step explanation:
For the first part of the expression, factor into (x+2)(x+1).
(x+2)(x+1)/(x+2)
The x+2 cancels out, so the answer is x+1
What is the explicit formula for the sequence: .25,5,1,2
The explicit formula for the geometric sequence is [tex]a_n=25(\frac{1}{5})^{n-1}[/tex].
What is explicit formula for geometric series?
The explicit formula for geometric sequence is [tex]a_n=a_1(r)^{n-1}[/tex] where r is common ratio.
Here the given sequence is 25,5,[tex]\frac{1}{2}[/tex]...
Here first term [tex]a_1=25[/tex]
Common ratio = [tex]$ \frac{a_2}{a_1}=\frac{5}{25}=\frac{1}{5}[/tex]
Now, Explicit formula [tex]$ a_n=a_1(r)^{n-1}[/tex]
=> [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex]
Hence the explicit formula of geometric series is [tex]$ a_n=25(\frac{1}{5})^{n-1}[/tex].
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Find the parametric equation of
X=4sin(5t)
Y=-48sin^2(5t)+8sin(5t)-3
The parametric equations for the curve are X = 4 sin(5t), Y = -48 sin²(5t) + 8 sin(5t) + 45
Describe Parametric Equation?A parametric equation is a set of equations that express the coordinates of a point as functions of one or more parameters. These equations define a curve or a surface in a space and are commonly used in mathematics, physics, engineering, and computer graphics to model and analyze various phenomena.
Parametric equations can be useful in many applications, such as modeling the motion of particles, designing curves and surfaces, and creating computer animations. They also allow for the visualization of complex shapes and curves that may be difficult to describe using traditional equations.
To find the parametric equation of the given curve, we need to express the coordinates x and y in terms of a parameter t. We can use the trigonometric identities to simplify the given equations and get:
X = 4 sin(5t)
Y = -48 sin²(5t) + 8 sin(5t) - 3
Let's start with Y. We can use the identity sin²(θ) + cos²(θ) = 1 to rewrite -48 sin²(5t) as -48 (1 - cos²(5t)) = -48 cos²(5t) + 48. Substituting this into the equation for Y, we get:
Y = -48 cos²(5t) + 8 sin(5t) - 3
Now, we can use another trigonometric identity, sin²(θ) + cos²(θ) = 1, to rewrite cos²(5t) as 1 - sin²(5t). Substituting this into the equation for Y, we get:
Y = -48 (1 - sin²(5t)) + 8 sin(5t) - 3
Y = -48 sin²(5t) + 8 sin(5t) + 45
So, the parametric equations for the curve are:
X = 4 sin(5t)
Y = -48 sin²(5t) + 8 sin(5t) + 45
This is the final answer.
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Benny purchased $400,000 of Peach Corporation face value bonds for $320,000 on November 13, 2020. The bonds had been issued with $80,000 of original issue discount (OID), because Peach was in financial difficulty in 2020. On December 3, 2021, Benny sold the bonds for $283,000 after amortizing $1,000 of the original issue discount.
What are the nature and amount of Benny's gain or loss?
Benny has a $fill in the blank 1
long-term capital loss
from the sale of the bonds.
Feedback Area
Feedback
NEED AWNSER ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPIdentify the formula used to find total surface area, then calculate total surface area. Select the appropriate choices.
Formula:
Total Surface Area:
The total surface area of the triangular prism is 556 unit²
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
The total surface area is the sum of each face area of the triangular prism. Hence:
Total surface area = [(1/2) * 8 * 17] + [(1/2) * 8 * 17] + (10 * 17) + (10 * 14) + (10 * 11) = 556 unit²
The total surface area is 556 unit²
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What is the average rate of change of sales between 2008 and 2010?
f(x)
495
513
410
402
520
580
631
719
624
582
X
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
HELP
Answer:
2008 and 2010 is 52 units per year.
Step-by-step explanation:
To find the average rate of change of sales between 2008 and 2010, we need to calculate the change in sales over that period, and divide by the time interval.
The sales in 2008 is f(2008) = 520, and the sales in 2010 is f(2010) = 624. The time interval is 2 years.
Therefore, the change in sales over that period is:
f(2010) - f(2008) = 624 - 520 = 104
The average rate of change of sales between 2008 and 2010 is:
(104) / (2) = 52
So the average rate of change of sales between 2008 and 2010 is 52 units per year.
Wesley is a member of the
kennel club in his area. His club uses
accordion fencing like the section shown
at the right to block out areas at dog
shows.
a. Identify two pairs of congruent
segments.
b. Identify two pairs of supplementary
angles.
The two pairs of congruent segments are PS = QR and PQ = SR
The two pairs of supplementary angles are P and Q; and S and R.
What are supplementary angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:
A + B = 180 degrees
For example, if angle A is 60 degrees, then its supplementary angle would be angle B, which is 120 degrees, because:
A + B = 60 + 120 = 180 degrees
Supplementary angles are commonly used in geometry and trigonometry to solve problems related to angles and lines. For instance, if two lines intersect, the opposite angles formed are always supplementary.
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Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is
x = 61 − p1
thousand units and the demand for brand 2 is
y = 71 − p2
thousand units, where
p1 and p2
are prices in dollars. If the joint cost function is
C = xy,
in thousands of dollars, how many of each brand should be produced to maximize profit?
brand 1=
Brand 2=
What is max profit?
To maximize profit, the manufacturer should produce 22 thousand units of each brand, and the maximum profit is:
Profit = (39 × 22) + (49 × 22) - (61 - 39)×(71 - 49) = $256 thousand.
What is profit?Profit is a term used in business and economics to refer to the amount of money or value that is gained after deducting the cost of production or acquisition from the revenue earned.
Mathematically, profit can be calculated as follows:
Profit = Revenue - Cost
To maximize profit, we need to determine the optimal values of P1 and P2. We can do this by setting up the profit function as follows:
Profit = Total Revenue - Total Cost
Profit = (P1 × x) + (P2 × y) - C
Profit = (P1 × (61 - P1)) + (P2 × (71 - P2)) - (61 - P1)×(71 - P2)
Taking the derivative of the profit function with respect to P1 and P2 and setting it equal to zero will give us the optimal values of P1 and P2 that maximize profit:
∂Profit/∂P1 = 61 - 2P1 + P2 = 0
∂Profit/∂P2 = 71 - 2P2 + P1 = 0
Solving these equations simultaneously, we get P1 = 39 and P2 = 49.
To find the quantities of each brand that should be produced, we can substitute P1 and P2 into the demand functions for x and y:
x = 61 - P1 = 22 thousand units of brand 1
y = 71 - P2 = 22 thousand units of brand 2
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f(x) = 2x^(2)-3x+6 find the value of f(-2)
Answer:
We can find the value of f(-2) by substituting -2 for x in the given function:
f(-2) = 2(-2)^(2) - 3(-2) + 6
= 2(4) + 6 + 6
= 8 + 12
= 20
Therefore, f(-2) = 20.
Step-by-step explanation:
Answer:
F(-2)=20
Step-by-step explanation:
You have to Substitute The X’s in your question with -2
This gives you: 2(-2)^2-3(-2)+6
2(-2)^2=2(4)=8 (Remember, A negative times a negative is a positive!)
-3(-2)=6
This leaves us with 8+6+6 which is equivalent to 20.
Colin's mom had a long day at work. "I feel like I drank 3 gallons of coffee today!" she joked. If she really drank that much coffee, how many times would she have filled her 12-fluid-ounce mug?
If Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.
What is multiplication ?
Multiplication is a mathematical operation that involves combining groups of equal sizes to find a total quantity. It is represented by the symbol "×" or "⋅" and involves two or more factors. The result of a multiplication operation is called the product.
1 gallon is equal to 128 fluid ounces, so 3 gallons is equal to 3 x 128 = 384 fluid ounces.
To find out how many times Colin's mom would have filled her 12-fluid-ounce mug, we divide the total amount of coffee by the size of the mug:
384 fluid ounces ÷ 12 fluid ounces/mug = 32 mugs
Therefore, if Colin's mom really drank 3 gallons of coffee, she would have filled her 12-fluid-ounce mug 32 times.
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Graph the line that passes through the points (-6, -8) and (3,-2) and determine
the equation of the line.
The weights for newborn babies is approximately normally distributed with a mean of 5.8 pounds and a standard deviation of 2.1 pounds.
Consider a group of 1100 newborn babies:
1. How many would you expect to weigh between 4 and 7 pounds?
2. How many would you expect to weigh less than 6 pounds?
3. How many would you expect to weigh more than 5 pounds?
4. How many would you expect to weigh between 5.8 and 10 pounds
Answer:
Step-by-step explanation:
To find the number of newborn babies weighing between 4 and 7 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.
For 4 pounds: z = (4 - 5.8) / 2.1 = -0.857
For 7 pounds: z = (7 - 5.8) / 2.1 = 0.571
Using the normal distribution table, the area between z = -0.857 and z = 0.571 is 0.5418.
So, the expected number of newborn babies weighing between 4 and 7 pounds is:
0.5418 x 1100 = 596 (rounded to the nearest whole number)
To find the number of newborn babies weighing less than 6 pounds, we need to calculate the z-score for 6 pounds and use the normal distribution table.
z = (6 - 5.8) / 2.1 = 0.095
Using the normal distribution table, the area to the left of z = 0.095 is 0.5375.
So, the expected number of newborn babies weighing less than 6 pounds is:
0.5375 x 1100 = 591 (rounded to the nearest whole number)
To find the number of newborn babies weighing more than 5 pounds, we need to calculate the z-score for 5 pounds and use the normal distribution table.
z = (5 - 5.8) / 2.1 = -0.381
Using the normal distribution table, the area to the right of z = -0.381 is 0.6499.
So, the expected number of newborn babies weighing more than 5 pounds is:
0.6499 x 1100 = 715 (rounded to the nearest whole number)
To find the number of newborn babies weighing between 5.8 and 10 pounds, we need to calculate the z-scores for these two weights and use the normal distribution table.
For 5.8 pounds: z = (5.8 - 5.8) / 2.1 = 0
For 10 pounds: z = (10 - 5.8) / 2.1 = 1.905
Using the normal distribution table, the area between z = 0 and z = 1.905 is 0.4713.
So, the expected number of newborn babies weighing between 5.8 and 10 pounds is:
0.4713 x 1100 = 518 (rounded to the nearest whole number)
Respass Corporation has provided the following data concerning an investment project that it is considering: Initial investment $ 160,000 Annual cash flow $ 54,000 per year Salvage value at the end of the project $ 11,000 Expected life of the project 4 years Discount rate 15% Click here to view Exhibit 14B-1 and Exhibit 14B-2, to determine the appropriate discount factor(s) using the tables provided. The net present value of the project is closest to:
NOTE : I got an overview of the answer BELOW BUT I want to clarify HOW THE ´´1.12´´ value is obtained please?
For me I would have had ´´1.15´´ (1+0.15 where 0.15 is the 15% discount rate).
Kindly help me to clarify this please.
EXPECTED ANSWER IS CORRECT: $516
The net present value οf the prοject is $516.
What is the net present value?A set οf cash flοws that happen at variοus dates are cοnsidered tο have a net present value οr net present wοrth. The amοunt οf time between nοw and a cash flοw determines the present value οf that cash flοw. The discοunt rate is anοther factοr. NPV takes the time value οf mοney intο the accοunt.
Here, we have
Respass Cοrpοratiοn has prοvided the fοllοwing data cοncerning an investment prοject that it is cοnsidering: Initial investment $ 160,000 Annual cash flοw $ 54,000 per year Salvage value at the end οf the prοject $ 11,000.
The prοject has annual inflοws οf $54,000 except in 4th year when it will have inflοws οf $65,000 because the salvage value will be added tο the inflοws.
Present value οf inflοws = 54,000/1.12 + 54,000/1.12² + 54,000/1.12³ + 65,000/1.12⁴
= $160,516
Net Present Value = 160,516 - 160,000
= $516
Hence, the net present value is $516.
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If h(x) = √6 +5f(x), where f(2)= 6 and f'(2) = 5, find h'(2).
Tip: 6 + 5f(x) is all under the square root.
By using the chain rule, we will see that the derivative is:
h'(2) = 5/12
How to find the value of h'(2)?Remember the chain rule, for the derivative of a composition of two functions f(x) and g(x), if we define:
k(x) = g(f(x))
Then:
k'(x) =g'(f(x))*f'(x)
In this case we know that:
h(x) = √(6 + 5*f(x))
We can define then:
g(x) = √(6 + 5x)
and write h(x) = g(f(x))
Now the differentiation will give:
h'(x) = (1/2)*(√(6 + 5f(x))⁻¹*f'(x)
Evaluating this in x = 2 we will get:
h'(2) = (1/2)*(√(6 + 5f(2))⁻¹*f'(2)
And we know that f(2) = 6 and f'(2) = 5
Then:
h'(2) = (1/2)*(√(6 + 5*6))⁻¹*5
h'(2) = (1/2)*(6)⁻¹*5 = 5/12
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A 6-meter roll of fabric costs $15.29. What is the unit price, rounded to the nearest cent?
Answer: $2.55
Step-by-step explanation:
Unit price = Total cost ÷ Length of fabric
$15.29 ÷ 6 = 2.54833333
Rounded to the nearest tenth is 2.55
A recipe for whole-grain bread calls for 1 oz of rye flour for every 4 oz of whole-wheat flour. How many ounces of each kind of flour should be used to make a loaf of bread weighing
37 oz?
Therefore, we need 7.4 ounces of rye flour and 29.6 ounces of whole-wheat flour to make a loaf of bread weighing 37 ounces, according to the recipe.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
Let's first assign variables to represent the amounts of rye and whole-wheat flour we need to use:
Let x be the number of ounces of rye flour.
Let y be the number of ounces of whole-wheat flour.
We know from the recipe that we need to use 1 oz of rye flour for every 4 oz of whole-wheat flour. This can be expressed as:
x = y/4 (equation 1)
We also know that the total weight of the loaf of bread should be 37 oz. This means that:
x + y = 37 (equation 2)
Now we can use equation 1 to substitute for x in equation 2:
y/4 + y = 37
Multiplying both sides by 4 to eliminate the fraction, we get:
y + 4y = 148
5y = 148
y = 29.6
So we need 29.6 ounces of whole-wheat flour. Using equation 1 to find x:
x = y/4 = 29.6/4 = 7.4
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The following data represent the number of grams of fat in breakfast meals offered at a local fast food restaurant. (a) Construct an ordered stem-and-leaf plot and (b) describe the shape of the distribution.
The stem and leaf plot for the data given is obtained as -
Stem Leaf
0 3 3 3 5 6
1 2 2 3 3 3 4 5 9
2 2 2 2 3 3
3 7 7 9
4 3
What is stem and leaf plot?
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
The data is given that represents the number of grams of fat in breakfast meals offered at a local fast food restaurant.
According to the data, the stem and leaf plot is -
Stem Leaf
0 3 3 3 5 6
1 2 2 3 3 3 4 5 9
2 2 2 2 3 3
3 7 7 9
4 3
The stem contains the first digits of the number, and the leaf plot contains the second digits of the number.
Therefore, the stem and leaf plot is obtained.
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