Loretta deposited $429 in a new savings account at Henry County Bank and Trust. She made no other deposits or withdrawals. After 6 months, the interest was computed at an annual rate of 6 .25%. How much simple interest did her money earn?
Please help???
Which of the following equations represents the graph shown?
A) f(x)=-x+2
B) f(x)=-x-2
C) f(x)=x+2
Okay it's not C, it's wrong
Answer:
the answer is f(x) = -x + 2
Step-by-step explanation:
because i got it right
sin pi/4 sin pi/6= 1/2(_____ pi/12-cos 5pi/12)
Answer:
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]
Step-by-step explanation:
We are given that
[tex] sin\frac{\pi}{4} sin\frac{\pi}{6}[/tex]
We have to correct value in blank space.
We know that identity
[tex] sin xsiny=\frac{cos(x-y)-cos(x+y)}{2}[/tex]
Using this identity
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{\pi}{4}-\frac{\pi}{6})-cos(\frac{\pi}{4}+\frac{\pi}{6})}{2}[/tex]
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{3\pi-2\pi}{12}-cos(\frac{3\pi+2\pi}{12})}{2}[/tex]
[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]
Answer:[tex] sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})[/tex]
There are two major tests of readiness for college, the act and the sat. act scores are reported on a scale from 1 to 36. the distribution of act scores are approximately normal with mean μ = 21.5 and standard deviation σ = 5.4. sat scores are reported on a scale from 600 to 2400. the sat scores are approximately normal with mean μ = 1498 and standard deviation σ = 316. alyssa scores 30 on the act. assuming that both tests measure the same thing, what score on the sat is equivalent to alyssa's act score? (round your answer to a whole number.)
Assuming that both tests measure the same thing, the equivalent sat score is 1994
The given parameters are:
ACT scores
Mean, μ = 21.5
Standard deviation, σ = 5.4
Score, x = 30
SAT scores
Mean, μ = 1498
Standard deviation, σ = 316
Start by calculating the z-score for the act score using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{30 - 21.5}{5.4}[/tex]
[tex]z = 1.57[/tex]
Next, calculate the z-score for the sat score using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{x - 1498}{316}[/tex]
Substitute 1.57 for z
[tex]1.57 =\frac{x - 1498}{316}[/tex]
Multiply both sides by 316
[tex]496.12 =x - 1498[/tex]
Solve for x
[tex]x = 496.12 + 1498[/tex]
[tex]x = 1994.12[/tex]
Approximate
[tex]x = 1994[/tex]
Hence, the equivalent sat score is 1994
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Final answer:
The equivalent SAT score to Alyssa's ACT score of 30 is calculated using Z-scores. The result is an SAT score of approximately 1996, rounded to the nearest whole number.
Explanation:
To determine what SAT score is equivalent to Alyssa's ACT score of 30, we use the concept of Z-scores. A Z-score represents the number of standard deviations an observation is from the mean of a distribution. The formula for calculating a Z-score is given by Z = (x - μ) / σ, where x is the score of interest, μ is the mean, and σ is the standard deviation.
First, we calculate the Z-score for Alyssa's ACT score:
ACT mean (μ) = 21.5
ACT standard deviation (σ) = 5.4
Alyssa's ACT score (x) = 30
Z-score for ACT = (30 - 21.5) / 5.4 ≈ 1.5741
Now we use Alyssa's ACT Z-score to find the equivalent SAT score by applying it to the SAT distribution. The SAT mean (μ) is 1498 and the SAT standard deviation (σ) is 316.Equivalent SAT score = SAT mean + (Z-score × SAT standard deviation)
Equivalent SAT score = 1498 + (1.5741 × 316) ≈ 1996
Therefore, rounding to the nearest whole number, the SAT score equivalent to Alyssa's ACT score of 30 is 1996.
gary father dropped him off soccer practice at2:45 pm .his mom picked him up at 5:00 pm.how long did soccer practice last
Uncle drew scored 28 pionts in 5 5\6 minutes how many points did he average
Approximately how many times greater is 4×107 than 8×103 ?
A.0.5
B.500
C.5000
D.50,000
40000000
8000
40000000 / 8000 = 5000
Answer is C. 5000
Tasha earns $400 per week plus a commission of 10% on her weekly sales. Each week she saves of her earnings. In the expression , what does the expression 400 + 0.1s represent in this situation?
3x3 systems answers 4x + 8y + z = 2 x + 7y - 3z = -14 2x - 3y + 2z = 3
Describe when you would need to solve a system of linear equations, instead of a single linear equation. (Site 1)
a single linear equation: you sell a budweiser for $3 a bottle & make $42.
a device: you promote budweiser for $3 and heineken for $4.
the entire wide variety of beers you promote is 10 and you make total of $forty.
what's linear equation components?The slope-intercept form of a linear equation is y = mx + b. in the equation, x and y are the variables. The numbers m and b deliver the slope of the line (m) and the fee of y when x is zero (b). The value of y whilst x is zero is known as the y-ithat ntercept due to the fact (zero,y) is the factor at which the road crosses the y-axis.
How do I solve linear equations?clean fractions or decimals.Simplify each aspect of the equation via doing away with parentheses and mixing phrases.Isolate the variable term on one side of the equation.remedy the equation by means of dividing each aspect of the equation.take a look at your solution.Learn more about linear equations here: https://brainly.com/question/1884491
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Which of the numbers below correctly describes 5,000 µf?
The number 5,000 µF represents a capacitance, indicating that the capacitor can store 5,000 microcoulombs of electric charge at an electric potential difference of 1 volt.
Explanation:The number 5,000 µF describes a capacitance. Capacitance is a measure of a capacitor's ability to store an electric charge. It can be defined as the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. So, when we say a capacitor has a capacitance of 5,000 µF (microfarads), it means the capacitor can store 5,000 micro coulombs of electric charge at an electric potential difference of 1 volt. It's important to know that the typical range of capacitors can vary from fractions of a picofarad (pF) to a milifarad (mF).
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what is the value of 6 in 89.6
What was the most direct effect of the establishment of the Queen’s Men?
a. New plays were written every year.
b. The queen visited Whitehall Palace.
c. The Puritans were outraged.
d. Drama received royal approval.
Answer:
C) The Puritans were outraged.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
trust
suppose each bag costs $14.99. estimate the total cost of 5 bags
5 hundreds 6 ten thousands 2 ones
Use cylindrical coordinates to evaluate the integral where d is the solid bounded above by the plane z=2 and below by the surface 2z=x2+y2
Answer:
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz = \frac{32 \pi}{5}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Multivariable Calculus
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \text{Region} \ D \left \{ {{2z = x^2 + y^2} \atop {z = 2}} \right.[/tex]
[tex]\displaystyle \iiint_D {z \big( x^2 + y^2 \big)^\big{\frac{-1}{2}}} \, dx \, dy \, dz[/tex]
Step 2: Find Volume Pt. 1
Find θ bound.
[Surface] Substitute in plane z:Find r bound.
[Surface] Substitute in plane z:Find z bound.
[Surface] Substitute in cylindrical conversions:Step 3: Find Volume Pt. 2
[Integrals] Substitute in cylindrical conversions:∴ the integral bound by region D is equal to [tex]\displaystyle \bold{\frac{32 \pi}{5}}[/tex].
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Topic: Multivariable Calculus
Unit: Triple Integrals Applications
Select from the drop-down menu to correctly identify the property shown.
(−5.2+ (−8.4)) + (−2.8) = −(5.2 + 8.4) + (−2.8)
Associative property
Commutative property
Opposite of sum property
Please help me, it's due tomorrow and I haven't gotten any sleep!!!! ); ); );
how to solve 4+2 - 5/6 - 1/2
Sara can type 90 words in 4 minutes about how many words would you expect her to type in 10 minutes at this rate
Answer:
C. 225 words
Step-by-step explanation:
90 / 4 = 22.5
22.5 x 10 = 225 words
Is the ratio 35 to 10 proportional to the ratio 7 to 5? Explain.
Identify the phrase that cannot be described by the same absolute value as the other three. Explain your reasoning.
Which shows the correct simplification of product of powers?
1.) 78 · 7-4 = 78· (–4) = 7–32
2.)78 · 7–4 = 78 ÷ (–4) = 7–2
3.)78 · 7–4 = 78 + (–4) = 74
4.)78 · 7–4 = 78 - (–4) = 712
The answer choice which shows the correct simplification of product of powers is:
78 · 7–4 = 78 + (–4) = 74What is Product of Powers?This refers to the mathematical property which states that when there is a multiplication of two powers that have the same base, then there would be the addition of exponents.
From the given choices, we can see that the powers are not given, so we can solve using inference.
This posits that (7^8) * (7^-4) was the product that was intended to be simplified and this law shows:
(A^m) * (A^n) = A^ (m+n)Hence, if we add the powers, then the correct answer would be option C because they are of the same base.
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addition or subtraction of unit fractions 1/2-1/8=
what symbol makes the statement true 307 324
A customer pays $1,100 in state taxes on a newly purchased car. What is the value of the car if state taxes are 8.9% of the value?
$9,765.45
$10,876.90
$12,359.55
$14,345.48
$15,745.45
Final answer:
To find the value of the car, divide the amount of state taxes paid by the tax rate percentage. The value of the car is $12,359.55.
Explanation:
To find the value of the car, we need to divide the amount of state taxes paid by the tax rate percentage. In this case, the state taxes paid is $1,100 and the tax rate is 8.9%.
So, the value of the car can be calculated as follows:
Value of the car = State taxes paid / Tax rate percentage
= $1,100 / 0.089
= $12,359.55
Therefore, the value of the car is $12,359.55
at a point P on the parabola x^2=4ay a normal PK is drawn. From vertex O, a perpendicular OM is drawn to meet the normal at M. Show that the equation of the locus of M as P varies on the parabola is x^4-2ax^2y+x^2y^2-ay^3=0
what inequality represents "a cat weighs no more than 8 pounds"
Final answer:
The inequality representing "a cat weighs no more than 8 pounds" is expressed as w ≤ 8, where w symbolizes the cat's weight in pounds. This concept illustrates how inequality symbols are applied in algebra to represent the relationship between quantities, applicable in various real-world scenarios.
Explanation:
The question asks which inequality represents "a cat weighs no more than 8 pounds." In mathematical terms, this statement can be translated using an inequality symbol that indicates the cat's weight is either equal to or less than 8 pounds. The appropriate symbol for this is “≤”, which stands for “less than or equal to.” Therefore, the inequality that represents this statement is w ≤ 8, where w represents the weight of the cat in pounds.
Using inequality symbols to show how two metric measurements are related is a foundational concept in algebra, and it is crucial when working with real-world scenarios where quantities have upper or lower bounds. For instance, understanding this concept can apply to various situations such as determining the weight of a dog, or comparing soda in a can to ensure it does not exceed a certain weight limit. It's important to grasp how these symbols convey relationships between quantities.
x2 + y2 – 10x + 6y = 15.
The cost of producing x pumpkin pies at a small bakery is given by c(x)=49+1.75x. Find the cost of producing 25 pies A. $74.00 B.$81.50 C.$92.75 D.$108.25
A function is defined as a relation between a set of inputs having one output each.
Input = 25 and output = $92.75
The cost of 25 pies is $92.75
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
Example: f(x) = 2 + 3x
x = 1
f(1) = 2 + 3x1 = 2 + 3 = 5
1 = Domain
5 = Range
We have,
c(x) = 49 + 1.75x
x = number of pies
The cost of producing 25 pies:
c(25) = 49 + 1.75 x 25
= 49 + 43.75
= $92.75
Thus the cost of 25 pies is $92.75
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