Solution
- The probability of him getting 1 queston correctly given tahat there is only one correct option out of 4 optins,
[tex]\begin{gathered} P(correct)=\frac{1}{4} \\ \\ P(incorrect)=1-P(correct) \\ P(incorrect)=1-\frac{1}{4}=\frac{3}{4} \end{gathered}[/tex]- Since here are questions, it implies that there are multiplye trials the student has.
Find the LCM of 18, 54, and 63.
Answer:
378
Step-by-step explanation:
Start with prime factoriazation
18 = 2 * 3 * 3
54 = 2 * 3 * 3* 3
63 = 3 * 3 * 7
2 * 3 * 3 * 3 * 7 = 378
For triangle ABC, ∡c=90°, b=5, and ∡A=72°. Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.
The angle A is given 72 degree and angle C is given 90 degree.
The side b is 5.
Then the right triangle is given
Use the property , the sum of the angles of the property is the 180 degree.
[tex]90^{\circ}+72^{\circ}+\angle B=180^{\circ}[/tex][tex]\angle B=180^{\circ}-90^{\circ}-72^{\circ}[/tex][tex]\angle B=18^{\circ}[/tex]Then the angle B is 18 degree.
Then to determine side a , use the tan trigonometric function.
[tex]\tan 72^{\circ}=\frac{a}{5}[/tex][tex]a=5\times tan72^{\circ}=15.38[/tex]The side a is 15.38.
Now to determine the side c, use the trigonometric function sin .
[tex]\sin 72^{\circ}=\frac{a}{c}=\frac{15.38}{c}[/tex][tex]c=\frac{15.38}{\sin 72^{\circ}}=16.18[/tex]The side c is 16.18.
Question
Gloria deposited $500 into a bank account that earned 7.5% simple interest each year. She earned $225 in interest before closing the account. No money was deposited into or withdrawn from the account.
How many years was the money in the account?
Round your answer to the nearest whole year.
Enter your answer in the box.
If Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
The deposited amount = $500
The simple interest = 7.5%
The interest she earned = $225
Then the final amount = The deposited amount + The interest she earned
= 500+225
= $725
The equation of simple interest
A = P(1+rt)
Where A is the final amount
P is the initial amount
r is the interest rate
t is the time period
725 = 500(1+(7.5/100)×t)
(1+0.075t) = 1.45
0.075t = 0.45
t = 0.45/0.075
t = 6 years
Hence, if Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years
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Simplify the expression. Show your work. Please help me!!!
[tex] \sqrt{ \frac{4 {x}^{2} }{3y} } \\ = \frac{ \sqrt{4 {x}^{2} } }{ \sqrt{3y} } \\ = \frac{ \sqrt{4 } \times \sqrt{ {x}^{2} } }{ \sqrt{3y} } \\ = \frac{2x }{ \sqrt{3y} } [/tex]
ATTACHED IS THE SOLUTION
Answer:
The image is the answer
Step-by-step explanation:
Write a recursive formula for the following arithmetic sequence.1, 12, -25, -38, ...a 1=an= for n ≧2
First, let's see the progression of the sequence of numbers
As you can see from the second term the sequence continues with a constant change of -13 which means d=-13.
The answers will be the expressions inside the red square box in each case.
A jet flies at an average speed of 230
miles per hour. How long will it take to
fly from New York to Amsterdam, a
distance of 3,647 miles? (distance =
rate time)
.
Answer:
15.9 hours.
Step-by-step explanation:
speed = distance / time.
230 = 3647 / time.
time = 3647 / 230.
time = 15.9 hours.
What is the solution to the system?
2x+3y=1
-2x-y=9
A (-7,5)
B (5,-3)
C (5,-7)
D (-3,5)
Answer:
A
Step-by-step explanation:
Adding the equations,
[tex]2y=10 \implies y=5 \\ \\ \therefore 2x+3(5)=1 \implies x=-7[/tex]
Consider the sample space of the following experiment:We roll two dice and each time we record numbers on both of them.How many elements are in the sample space?
Answer: 36
One die has a total outcome of 6 elements (1, 2, 3, 4, 5, 6). Now, if we roll two dice, each time you roll a number on the first die, there are another 6 possible outcomes for the second die.
Therefore, the number of elements in the sample space would be:
[tex]6\times6=36[/tex]There would be 36 elements in the sample space.
Carson Company has an inventory turnover of 13.00, and its inventory amounts to $5,000,000. What is the amount of cost of goods sold?
$6,50,000 is the cost of the goods sold.
What is Inventory turnover?By dividing a company's cost of sales, or cost of goods sold, by its inventory turnover, one can determine how well it uses its inventory (COGS).
The number of times inventory is sold or used over a given time frame, like a year, is referred to as the inventory turnover in accounting. It is calculated to determine whether a company has an excessive amount of inventory in relation to its level of sales.
Inventory turnover is the count of times a company's stock is sold during the course of a month, a quarter, or (most frequently) a year of business.
We should apply the following formula to calculate the cost of goods sold:
Cost of goods sold / inventory equals inventory turnover.
Rearranging the equation and replacing the unknown values results in:
Inventory plus inventory turnover equals cost of goods sold.
Price of items sold = $5,000,000 divided by 13
$6,50,000 is the cost of the goods sold.
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a local boys club sold 156 bags of mulch and made a total of $455 it's sold two types of mulch hard word for $3.25 a bag in Pine Box for $2.75 a bag how many bags of each kind did it sell
Let's define first the variables.
let H be the number of bags of the type that cost 3.25 and P the number of bags of the type that cost 2.75.
since they sold a total of 156 bags we have that H+P=156
and from the other condition we obtain 3.25H+2.75P=455
now we can solve the system of equations.
from the first equation H=156-P
substituing the previous equality in the second one we obtain:
[tex]3.25(156-P)+2.75P=455[/tex][tex]507-3.25P+2.75P=455[/tex][tex](2.75-3.25)P=-53[/tex][tex]0.5P=53[/tex][tex]P=106[/tex]now that we have P, we can replace it in the first equation obtaining that H=50
then the answer will be that they sold 50 bags of $3.25 and 106 bags of $2.75
If g(x)=5 x, h(x)= √ x, find the composition.
(g ° h)(0)
(g ° h)(0) = ____
The value of the composite function (g ° h)(0) is equivalent to zero.
Composite functionsA function that is composed of further functions, each of which serves as the input to the next.
Given the function below;
g(x) = 5x
h(x) = √x
Determine the composite function (g o h)(x)
(g o h)(x) = g(h(x))
(g o h)(x) = g(√x)
g(√x) = 5√x
Substitute the value of x to have:
(g o h)(0) = 5√0
(g o h)(0) = 0
This gives the required value
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Write the equation x2 + y2 + 6x + 8y + 24 = 0 in vertex form.
ANSWER
[tex](x+3)^2+(y+4)^2=1[/tex]EXPLANATION
We want to write the equation of the circle in vertex form:
[tex]x^2+y^2+6x+8y+24=0[/tex]The first step is to group the x terms and y terms together and take the constant to the right-hand side of the equality sign:
[tex]x^2+6x+y^2+8y=-24[/tex]Now, complete the square for the x terms:
[tex]\begin{gathered} x^2+6x+(\frac{6}{2})^2+y^2+8y=-24+(\frac{6}{2})^2 \\ x^2+6x+9+y^2+8y=-24+9 \\ (x+3)^2+y^2+8y=-15 \end{gathered}[/tex]Repeat the process for the y terms:
[tex]\begin{gathered} (x+3)^2+y^2+8y+(\frac{8}{2})^2=-15+(\frac{8}{2})^2 \\ (x+3)^2+y^2+8y+16=-15+16 \\ (x+3)^2+(y+4)^2=1 \end{gathered}[/tex]That is the equation of the circle in vertex form.
What is the image point of (-1, -3) after the transformation D₂ o T 4.-5?
The image of the point after the transformation is (2, -7)
How to image of the point after the transformation?The given parameters are:
Point = (-1, 3)
Transformation rule:
D₂ o T 4.-5
The above means that
Dilation by a scale factor of 2Followed by a translation of (4, -5)When these transformations are combined, we have
(x, y) = (2x + 4, 2x - 5)
So, the mathematical representation of this transformation is
(x, y) = (2x + 4, 2x - 5)
Substitute the equation Point = (-1, -3) in the equation (x, y) = (2x + 4, 2x - 5)
So, we have the following equation
(x, y) = (2(-1) + 4, 2(-1) - 5)
Evaluate the product
(x, y) = (2, -7)
Hence, the image is (x, y) = (2, -7)
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Calculate the standard score of the given X value, X=83, where μ=88.1 and σ=87. Round your answer to two decimal places.
The standard score for the given X value is -0.06
Standard Score
Standard score or Z - Score is inversely varies with the standard deviation and directly varies with the difference of the raw score and the mean score.
The formula to calculate standard score is
z - score = (X - μ)/σ
Where
Z = standard score
x = observed value
μ = mean of the sample
σ = standard deviation of the sample
Given,
Here we have the value of X = 83, μ=88.1 and σ=87.
Now, we need to find the standard score for this values and we have also round off the result to two decimal places.
Apply the given values on the z-score formula, then we get,
z-score = (83 - 88.1)/87
When we simplify the numerator, then we get,
z - score = -5.1/87
After the division of these numbers we get the value of z-score as,
z - score = -0.0586
When we round off the result into two decimal place then we get the value of standard score as -0.06.
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Factor: x(3y-5)+3(3y-15)
3xy-5x+9y-45
Step-by-step explanation:
Step by Step Solution
STEP1:STEP2:Pulling out like terms
2.1 Pull out like factors :
3y - 15 = 3 • (y - 5)
Equation at the end of step2: (x • (3y - 5)) + 9 • (y - 5) STEP3:Equation at the end of step 3 x • (3y - 5) + 9 • (y - 5) STEP4:Trying to factor a multi variable polynomial
4.1 Split 3xy-5x+9y-45
4.1 Split 3xy-5x+9y-45
into two 2-term polynomials
-5x+3xy and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy-5x and +9y-45
This partition did not result in a factorization. We'll try another one:
3xy+9y and -5x-45
This partition did not result in a factorization. We'll try another one:
3xy-45 and +9y-5x
This partition did not result in a factorization. We'll try another one:
-45+3xy and +9y-5x
This partition did not result in a factorization. We'll try
what is the distance between point A (-1, 3) and point B(-8, 3. A 2 units B 5 units C 7 units D 9 units.
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total ofapplication
Problem
At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain?
Solution
For this case we can set up the following notation
x= number of cheeseburgers
y= small fries
4x +5y= 2310
3x + 2y= 1330
From the first equation we can solve for x and we got:
x= 577.5 - 5/4 y
And now we can replace this into the second equation and we got:
3(577.5 -5/4 y) +2y= 1330
And we can solve for y:
1732.5 - 15/4 y + 2y = 1330
-7/4 y = -402.5
y= 230 cal
And solving now for x we have:
x= 577.5 - 5/4 (230) = 577.5 - 287.5 = 290 cal
Solve for x. Represent your answer on a number line.½x − 3 < − 4
The equation is
[tex]\frac{1}{2}x-3<-4\Rightarrow\frac{x}{2}<-4+3\Rightarrow\frac{x}{2}<-1\Rightarrow x<-2[/tex]Therefore x<-2. The number line representation is
You want to buy new kitchen appliances 3 years from now, and you plan to save $3,000 semiannually, beginning immediately. You will deposit your savings in an account that pays 7.2% interest. How much will you have 3 years from now?
The final amount after 3 years compounded semi-annually is $3709.20
Compound Interest
To solve this problem, we simply need to use compound interest formula which is given as
[tex]A = p(1 + \frac{r}{n})^n^t[/tex]
where
A = final amountP = initial amount or principalr = rate n = number of times compoundedt = timeLets substitute the values into the formula and solve
[tex]A = p(1 + \frac{r}{n})^n^t\\A = 3000(1 + \frac{0.072}{2})^2^*^3\\ A = 3709.20[/tex]
The amount accrued 3 years from now is $3709.20
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Graph the line that is parallel to the line
2x-3y = -9 and passes through the
point (-3, 5).
y = 2/3x + 7 is slope-intercept form of the equation .
What exactly does slope intercept mean?
A method of expressing a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form.The point where the line is drawn the y-axis is known as the y-intercept, and the slope refers to how steep the line is.the equation of the parallel line in slope intercept form y=mx+b so that we can clearly see the slope and y intercept
2x-3y = -9
3y = 2x + 9
y = 2/3x + 9/3
y = 2/3x + 3
compare equation y = mx + c
slope = 2/3
to find c put x = -3 and y = 5
y = mx + c
5 = 2/3 * (-3) + c
5 = -6/3 + c
c = 5 + 2 = 7
put the final equation together
y = 2/3x + 7
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Which of the following equations is not exponential?
Y=1^x
Y=(1/2)^x
Y=-2^x
The first equation given in the question as, y = 1^x is not exponential.
What do you mean by exponential?
A mathematical function with the form f (x) = a^x is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's base and must be bigger than 0. The transcendental no., or roughly 2.71828, is the most often used exponential function on regular basis.
The equation, y = 1^x is not an exponential because for any integer value of x, y always equals to zero. Which makes it simple equation and not an exponential equation.
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What number should go in the gap to factorise this expression?
6x+14= (3x+7)
The number that should go in the gap to factorise the given expression is 2
Factorizing an expressionFrom the question, we are to determine the number that should go in the gap in order to factorise the given expression.
The given expression is
6x + 14
To determine the number that should go in the gap,
First we will factorize the given expression
6x + 14
The greatest common factor (GCF) of 6 and 14 is 2
Thus,
We can factor out 2 as follows
2(3x + 7)
The factored form of the expression is 2(3x + 7)
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Write each rational number as a decimal. If there’s no phone number, make sure to include a zero in the beginning. So if your answer is 0.7 make sure to put the zero in the beginning.
Calculate the given division, as shown below
Therefore, 33/40 is equal to 0.825. The answer is 0.825
5. Stabiliţi dacă numerele următoare sunt prime: 37, 93, 123, 377, 602, 769, 1 243, 1999.
Answer:
Numere prime:37,377,769,1243,1999
Sunt numere prime deoare au ca divizori doar 1 si ei insusi
FIND SLOPE AND Y INTERCEPT EASY QUESTION WILL GIVE BRAINLIEST ANSWERRRR HELPPP URGENT DUE IN A FEW MINUTESS
Simplify the equation 4x+9y = -9 in slope-intercept form of equation.
[tex]\begin{gathered} 4x+9y=-9 \\ 9y=-4x-9 \\ y=-\frac{4}{9}x-\frac{9}{9} \\ =-\frac{4}{9}x-1 \end{gathered}[/tex]So slope of line is -4/9 and int
Line a is parallel to line b. Line a contains the points (3, 4) and (6, 7). Line b contains the points (2,8) and (6. y). What is the value of y?A7B11С12D24
parallel lines have the same slopes. Therefore,
[tex]m_1=m_2_{}_{}_{}[/tex][tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{7-4}{6-3}=\frac{3}{3}=1[/tex][tex]m_2=1[/tex]Y can be found below
[tex]\begin{gathered} 1=\frac{y-8}{6-2} \\ 1=\frac{y-8}{4} \\ 4=y-8 \\ y=4+8 \\ y=12 \end{gathered}[/tex]online you found the shoes you want to buy for 30% off the regular price is $150. this is the first time you have ordered from this site they're offering an additional 20% off for the first time customers was your final price list shoes after the discounts?
If we apply the first discount the shoes would have a price of:
[tex]150-150\cdot0.3=105[/tex]To this pice we make the 20% discount, then:
[tex]105-105\cdot0.2=84[/tex]Therefore, after the discounts the price would be $84
Which expression is equivalent to -0.26v + v - 0.07?(answer choices are below)
To simplify the expression
-0.26v + v - 0.07
we will only add the ones with variable v
0.74v -0.07
The correct option is
0.74v - 0.07
t hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartbozn, and the radius of the shaded region Is 2 in.the value 3.14 for T. Round your answer to the nearest hundredth.
Given:
Required:
To find the probability that the dart land will be in the shaded region.
Explanation:
Area of the circle is given by the formula:
[tex]A=\pi r^2[/tex]Where r = radius
Thus the area of the circular region
[tex]\begin{gathered} =(3.14)\times(2)^2 \\ =3.14\times4 \\ =12.56\text{ square in.} \end{gathered}[/tex]The area of the square is given by the formula:
[tex]=(side)^2[/tex]Thus the area of the given square
[tex]\begin{gathered} =(6)^2 \\ =36\text{ square in.} \end{gathered}[/tex]The probability of an event is given by the formula:
[tex]P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]The probability that the dart land will be in the shaded region
[tex]=\frac{Area\text{ of the shaded region}}{Area\text{ of the square}}[/tex]Thus probability
[tex]\begin{gathered} P=\frac{12.56}{36} \\ P=0.3488 \\ P=0.349 \end{gathered}[/tex]Final answer:
Thus the probability that the dart land will be in the shaded region is 0.349.
Which of the following criterion will accurately complete the proof in step 4
2.
[tex]\begin{gathered} \angle RAG\text{ and }\angle RET\text{ are vertical angles} \\ \Rightarrow\angle RAG\cong\angle RET \end{gathered}[/tex]The reason for 2 is 'the angles are vertical'.
3. In the diagram below, we can identify the alternate interior angles more easily
Therefore, Therefore, the statements of the third step are
[tex]\begin{gathered} \angle AGR\cong\angle ETR \\ \text{and} \\ \angle GAR\cong\angle\text{TER} \end{gathered}[/tex]Finally, the corresponding angles of triangles GRA and TRE are all congruent; thus, the two triangles are congruent because of the AA similarity criterion. The answer is AA similarity criterion. The length of the sides is not involved in the demonstration.