The quantity of sugar required to make 78 cookies is 8.1 cups.
Given that, you need 1.25 cups of sugar to make 1 dozen cookies.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
The quantity of sugar to make 1 cookie
= 1.25/12
= 0.10417
The quantity of sugar to make 78 cookies
= 78×0.10417
= 8.1 cups
Therefore, the quantity of sugar required to make 78 cookies is 8.1 cups.
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assume that the box confains 11 balls: 5 red, 3 blues, and 3 yellow. as in the text, you draw one ball, note its color, and if its yellow rrplace it. if it is not yellow you do not replace it. you then draw a second ball and note its color
The probability that the second ball drawn is yellow is of:
0.2926 = 29.26%.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In this problem, the possible outcomes to obtain a yellow ball on the second draw are:
Yellow (3/11 probability) then yellow (3/11 probability). -> yellow on the first is replaced.Non-yellow (8/11 probability) then yellow (3/10 probability) -> non yellow on the first is not replaced.Then the probability of an yellow ball on the second draw is given as follows:
p = (3/11) x (3/11) + (8/11) x (3/10) = 0.2926 = 29.26%.
Missing InformationThe problem asks for the probability that the second ball drawn is yellow.
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Finding missing side length given two similar triangles
Value of BC is 36 in triangle's similarity .
What is the triangle's similarity?
If one of the following conditions is satisfied by two triangles, they are comparable. There is equality between two sets of matching angles. It is proportionate to have three sets of comparable sides. In addition to being proportional and having equal corresponding angles, two pairs of corresponding sides are also identical.ΔABC and ΔPQR are similar .
so all sides are equal in ratio .
let BC is x .
AB/BC = PQ/QR
18/x = 2/4
18 * 4 = 2 * x
x = 18 * 4/2
x = 18 * 2
x = 36
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Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Since corresponding parts of
congruent triangles are congruent, angle ZWY is congruent to angle XWY and angle ZYW is congruent to angle XYW.
True or False: Mai can now conclude that diagonal WY bisects angles ZWX and ZYX.
True
O False
It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX
Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:
Diagonal WY bisects angles ZWX and ZYX because:
all corresponding parts of both triangles are congruent. (Option A).
If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.
Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.
If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).
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2
Linda paid $5.50 for 4 pounds of
strawberries. How much did she pay
per pound of strawberries?
She paid $1.375 per pound of strawberries.
What is the unit rate?
When expressed rate as a fraction, a unit rate has a denominator of 1.
Since 4 pounds cost $5.50, 1 pound of strawberries will cost 5.50/ 4 ≈ $1.375.
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Solve 2x2 + 20x + 8 = 0 by completing the square.
Answer:
x=−5+ 21 ,−5− 21
Step-by-step explanation:
x= 4−20+4= 214−20−4 =21
Jeffrey earns a constant hourly rate of $12.25 at the tire shop. Which of these best represents the relationship between the number of hours Joseph worked, h, and his total amount earned, t?
Answer:
The correct equation is t = 12.25h.
Use the quadratic formula to solve for the "solutions", or "zeros" of the equation. Did
you get 2 real answers, I real answer, or 2 imaginary answers?
Show your work F(x) =3x^2 - 40x + 180
We get 2 complex answers
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.
Given that F(x) = 3x2 - 40x + 180
Set F(x) to 0, and you get ax2 + bx + c = 3x2 -40x + 180.
[-b +/- (b2 -4ac)(1/2)] is the quadratic formula. / 2a.
The stuff under the square root / radical (b2 - 4ac) is the KEY to your answer, and it determines whether you have two real, one real, or two imaginary answers. The discriminant is the term (b2 - 4ac).
Obviously, if (b2 - 4ac) > 0, you have two real answers, because the square root of a positive number is also a (positive) real number. And -b multiplied by a real number (and divided by 2a) yields two (real) answers.
If (b2 - 4ac) = 0, you have one correct answer because the square root of 0 is zero. And -b multiplied by a 0 real number (and divided by 2a) yields 1 (real) answer.
(b2 - 4ac) 0 yields two fictitious answers, because the square root of a negative number is a fictitious number. And -b multiplied by an imaginary number (and divided by 2a) yields two (complex) answers.
In this case, (b2 - 4ac) = ((-40)2 - 4(3)(180)) = 1600 - 2160 0 As a result of the discriminant is negative, the quadratic formula yields two complex answers.
Therefore we get two complex answers
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Answer:
[tex]x=\dfrac{20 +2\sqrt{35}\:i}{3}, \quad x=\dfrac{20 -2\sqrt{35}\:i}{3}[/tex]
2 imaginary answers.
Step-by-step explanation:
Given quadratic function:
[tex]f(x) =3x^2 - 40x + 180[/tex]
The zeros of a quadratic function can be found when f(x) = 0:
[tex]\implies 3x^2 - 40x + 180=0[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore:
a = 3b = -40c = 180Substitute the values of a, b and c into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-(-40) \pm \sqrt{(-40)^2-4(3)(180)}}{2(3)}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{1600-2160}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{-560}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{16 \cdot 35 \cdot -1}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm \sqrt{16}\sqrt{35}\sqrt{-1}}{6}[/tex]
[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\sqrt{-1}}{6}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex]:
[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\:i}{6}[/tex]
[tex]\implies x=\dfrac{20 \pm 2\sqrt{35}\:i}{3}[/tex]
Therefore, the solution is 2 imaginary answers.
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].
An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].
What transformation takes the graph of f(z) - 4z +9 to the graph of g (z) = 4x+7?
translation 2 units right
translation 2 units left
translation 2 units down
translation 2 units up
The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)
What transformation rule is used to transform a given function?
In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.
Horizontal translation
g(x) = f(x - k), where k > 0 for a translation in + x direction.
Vertical translation
g(x) = f(x) + k, where k > 0 for a translation in + y direction.
After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down. Then, we find the following transformation formula:
g(z) = f(z) - 2
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Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years with monthly compounding?
Round your answer to the nearest cent.
Do NOT round until you calculate the final answer
Correct answer: $7,434.57
Answer:
amount owed = $7434.57
Step-by-step explanation:
To solve this problem, we have to use the following formula:
[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],
where:
• A = final amount
• P = principal (initial) amount
• r = annual interest rate
• n = amount of times the interest is compounded per time period
• t = number of years the money is kept for
In this case, the principal amount, P = $5000 and the money is owed for two years, so t = 2. The annual interest rate, r = 0.20 (20% = [tex]\frac{20}{100}[/tex] = 0.2). The interest is compounded monthly, which means it is compounded 12 times per year. Therefore, n = 12.
Using the above information and formula, we can calculate the amount owed after 2 years:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]= 5000(1 + \frac{0.2}{12})^{12 \times 2}[/tex]
[tex]=[/tex] $7434.57
Therefore, the amount Edgar owes after 2 years is $7434.57.
Evaluate (6x+3y)-z^(2)÷(2x) when x=-3,y=4,z=-6
24.
Step-by-step explanation:1. Write the expression.[tex](6x+3y)-\frac{z^{2}}{(2x)}[/tex]
2. Substitute the variables by the respective given value using parenthesis.[tex](6(3)+3(4))-\frac{(6)^{2}}{(2(3))}[/tex]
3. Simplify the expression by applying the hierarchy or mathematical operations.a) Solve parenthesis.
[tex](18+12)-\frac{(6)^{2}}{6}\\ \\30-\frac{(6)^{2}}{6}[/tex]
b) Solve the exponent.
[tex]30-\frac{36}{6}[/tex]
c) Divide.
[tex]30-6[/tex]
d) Subtract.
[tex]24.[/tex]
A die is continuously rolled until the total sum of all rolls exceeds 150 What is the probability that at least 40 rolls are necessary?
The probability that at least 40 rolls are necessary is 4/15.
What is probability?
Probability shows the likelihood of an event happening. it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1
Probability P=no. outcomes/total no. of the possible outcomes
From the question;
No of out comes=40
No. of total possible outcome=150
Therefore probability P= 40/150
P=4/15
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The average weight of a population of manatees is unknown. A random sample of manatees selected from the population yields a sample mean of x¯=880.3 pounds. Assume the sampling distribution of the mean has a standard deviation of σx¯=10.4 pounds. Use the Empirical Rule to construct a 68% confidence interval for the true population mean weight.
The confidence interval that we have for the population mean is given as [869.9 , 890.7]
How to solve for the confidence intervalThe confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.
We have the following data that we have to solve this problem with
The mean = x¯=880.3 pounds
The standard deviation = 10.4 pounds.
The confidence interval = 68%
To get the confidence interval for the true mean of the population weight we would have
mean ± standard deviation
880.3 ± 10.4
The interval would be written out as
880.3 - 10.4 and 880.3 + 10.4
the confidence interval =
[869.9 , 890.7]
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2. Solve the application problem.
Find the area of a mirror that measures 2 yards by 7/8 yard.
A. 1 3/4 yd^2
B. 5 3/4 yd
C. 1 3/4 yd
D. 5 3/4 yd^2
Answer:
Area = l × w
= 2 × 0.875
= 1 3/4 yd^2 or 1.75 yd^2
hope i helped
Step-by-step explanation:
David weighed himself each week and recorded a gain of 3.5 pounds, a loss of 8.6 pounds, a loss of 2.1 pounds and a gain of 1.4 pounds. What is David’s overall gain/loss of weight?
Using simple mathematical operations, David's overall loss is -5.8.
What do we mean by mathematical operations?Calculating a value while using operands as well as a math operator is known as a mathematical "operation."The supplied operands or integers must comply with a specified set of standards pertaining to the symbol of the math operator.A rule that outlines the appropriate procedures to follow when examining a mathematical equation is known as the order of operations.You can recall the PEMDAS actions parenthesis, exponents, multiplication, dividing (from Left to Right), adding, and subtracting in this order (from left to right).So, the overall gain/loss of David is:
Gain: 3.5 pounds, 1.4 poundsLoss: 8.6 pounds, 2.1 poundsNow, calculate loss/gain as follows:
3.5 + 1.4 - 8.6 - 2.14.9 - 10.7- 5.8Therefore, using simple mathematical operations, David's overall loss is -5.8.
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Select all possible solutions to the equation (x - 5)² - 6 = 0.
The two possible solutions of the given quadratic equation are -
x = +√6 +5 and x = -√6 +5
What is defined as the solution of equation?Finding the value that a variable expresses is the process of solving an equation. The solution of the equation is the value that was discovered. The collection of all values which, when substituted for unknowns, cause an equation to hold true is known as the solution. Two fundamental algebraic rules using the additive property as well as the multiplicative property are utilised to determine the solutions for equations having an unique unknown raised to a power of one.For the given question;
(x - 5)² - 6 = 0
Bring constant on other side.
(x - 5)² = 6
Taking square root both side.
√ (x - 5)² = √6
(x - 5) = ±√6
Separate the constant and variables.
x = ±√6 +5
There are two possible solution.
x = +√6 +5 and x = -√6 +5
Thus, the two possible solutions of the given quadratic equation are -
x = +√6 +5 and x = -√6 +5.
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What is [tex]\frac{1000}{\frac{4}{3}\pi }[/tex]
The result of the expression as given in the task content is; 750/π.
What is the result of the quotient?It follows from the task content that the result of the division operation as given in the task content is to be determined.
Given the expression; 1000 ÷ (4/3)π
The expression can therefore be rewritten as follows;
1000 × (3/4) π
Hence, we have;
3000/4π
By further simplifying the expression; we have;
750/π
Hence, the result of the division as given in the task content is; 750/π.
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please help and please use the diagram
7
8
9
Answer:
↓ ↓ ↓
Step-by-step explanation:
7) Name of plane to piano CIJ:-
Plane AGL8) Name a segment parallel to BC:-
FE9) Which segment is not skew to EK:-
C. CI______________________
Hope this helps!
Have a great day!
pls help with this . give only what it ask for the answers.
Answer:
(10, -1)
Step-by-step explanation:
x + 2x = 3x
-y + y = 0
11 + 19 = 30
3x = 30
3/3 x = 30/3
x = 10
10 - y = 11
y = -11 + 10
y = -1
9. The sum of two numbers is 130 and their difference is 34. Let x be the first number and y be the second
number. Set up a system of equations and use the elimination method to find the numbers. You must
show your work.
Using the system of equations and use the elimination method the two numbers are 82 and 48.
What is the elimination method?
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are equal.
Here, we
let the first number = x
let the second number = y
according to the given conditions:
x + y = 130 ........(1)
x - y = 34 .........(2)
Using the elimination method we add both equations (1) and (2) and we get
2x = 164
x = 164/2 = 82
Now, we substitute the value of x in eq (1) and we get
82 + y = 130
y = 130-82
y = 48
Hence, using the system of equations and use the elimination method the two numbers are 82 and 48.
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(b)
The table below shows the cost price, selling price and profit or loss as a percentage of the cost
price.
Complete the table below, inserting the missing values at (i) and (ii).
(i)
(ii)
Cost Price
$55.00
(c) The table shows some rates of exchange :
Calculate the value of
(i) EC $ 1 in TT $......
(ii) US $80 in EC $ .
(iii) TT $648 in US $. .....
Selling Price
$44.00
$100.00
US $1.00 = EC $2.70
TT $1.00 = EC $ 0.40
Percentage
Profit or Loss
25% profit
(4 marks)
. (1 mark)
. (1 mark)
...... (3 marks)
Total 12 marks
Answer:
US$1.00=EC$2.70 TT$1.00=EC$0.40 calculate the value of : 1.EC$1in TT$ 2.US$80inEC$ 3.TT$648 in US$
Step-by-step explanation:
that what i've got is that I hope that helps you
A pet store has 7 cats. Here are their weights (in pounds).
14, 11, 10, 10, 6, 8, 14
Send data to calculator
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
pounds
To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.
(12+16+10+8+14+15)/6
= 75/6
= 12.5 (answer is already rounded to nearest tenth)
If you make $4 on a sale of one share of stock that you bought for $22, what is your ROI?
Answer:
$26
Step-by-step explanation:
Type in only your numerical answer to the given problem if G(x)=x^2-5, then g(3)=?
helpppp please??? brainlesttttt
Find x in this equation.
3/8 = 15/5x - 2
Answer:
x=19/24
Step-by-step explanation:
3/8=15/5x-2
3/8= 3x -2 |*8
3=24x-16
24x=19
x=19/24
rajesh is working out the are of the cirle with radius 10 he writes area=3.142x20 explain why rajesh is wrong
Answer:
100π = 314.1592654
Step-by-step explanation:
area of a circle πr²
π×10²
10×10 =100
100×π
Evaluate this expression. (6x103) ÷ (3x102) express your answer in scientific notation.
9514 1404 393
Answer:
2×10¹
Step-by-step explanation:
For division, mantissas divide, and exponents subtract.
Answer:
2*10^1
Step-by-step explanation:
Process
When you divide powers, they can be subtracted -- numerator - denominator in powers
The numbers divide the way you normally would if the question is 6/3 = 2
Numerator power = 3
denominator power = 2
Solution
6*10^3/ 3*10^2 = (6/3) * 10^(3 -2) = 2 * 10^1 = 20
20 = 2 * 10^1
x-intercept of (y+12) = 3(x - 9)
Answer: purple is the greatest
student enrollment at a local school is concerning because the number of student has dropped to 504, which is 20% decrease from the previous year. what was the student enrollment the previous year?
The student enrollment the previous year is 630 students.
How to calculate the number of students?Sine the percentage given is 10% decrease, us implies that the percentage for the previous year will be x
Based on the information given, this will be illustrated as:
x - (20% × x) = 504
x - 0.2x = 504
0.8x = 504.
Divide.
x = 504 / 0.8
x = 630
There were 630 students.
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The municipal swimming pool in Charlotte, North Carolina has three different ways of paying for individual open swimming. Nick is trying to decide which way to pay.
Early Pay: Pay $110.00 before Memorial Day; swim any number of days
Deposit Plus: $30.00 deposit plus $6.00 per day
Daily Pay: $9.00 per day
Write an equation for each method of payment. Write your equations in slope-intercept form so that x is the number of days and y is the cost.
a. Early Pay:
b. Deposit Plus:
c. Daily Pay:
the answer must be a y=mx+b equation for a b and c
The equations for early pay, deposit plus and daily pay is y = 110, y = 6x + 30 and y = 9x respectively.
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Let y represent the total cost for swimming x numbers of days.
Early Pay: Pay $110.00 before Memorial Day; swim any number of days. Hence:
y = 110
Deposit Plus: $30.00 deposit plus $6.00 per day. Hence:
y = 6x + 30
Daily Pay: $9.00 per day. Hence:
y = 9x
The equation for early pay is y = 110
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