A package of 3 pairs of insulated socks costs $15.87. What is the unit price of the pairs of socks?
The unit price is $
per pair of socks.
A package of 3 pairs of insulated socks costs $15.87, thus the unit price of the pair of socks can be calculated as $5.29 via the unitary method.
What is Unit Price?A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities.
Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.
What does "unit pricing" mean?A price stated in terms of a certain amount per predetermined or standard unit of good or service agreed to purchase the gravel for 50 cents per yard.
Frequently a price that is quoted that includes both the base unit of the good or service and any additional costs (such as shipment or installation).
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Let p: The shape is a rhombus.
Let q: The diagonals are perpendicular.
Let r: The sides are congruent.
Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?
p ∧ (q ∧ r)
(p ∨ q) ∨ r
p ↔ (q ∧ r)
(p ∨ q) ↔ r
The correct representation of statement ''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent'' will be;
⇒ p ↔ (q ∧ r).
What is Logic operators?
A symbol or words to use to connect two or more expressions are called Logic operators.
Given that;
The statement is,
''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent''
Now,
Since, The word ''if and only if'' is represent by using the biconditional logic operator (↔) and the word ''and'' is represented by using the logical conjunction operator (∧).
So, The logic representation of the statement;
"The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent” will be;
⇒ p ↔ (q ∧ r).
Thus, The correct representation of statement ''The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent'' will be;
⇒ p ↔ (q ∧ r).
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The area of a triangle is given by A = 1/2bh, where b is the base and h is the height of the triangle
The area of the triangle with base 12 units, and height of 3 units is: B. 18.
How to Determine the Area of a Triangle?To find the area of a triangle, find the height, which is the distance from its base to its highest point, and also find the length of the base of the triangle, then apply the formula below:
Area of triangle = 1/2 × base × height
From the information given, the following are the parameters we will need to work with:
Base of the triangle = QR = 12 units
Height of the triangle = PH = 3 units
Plug in the values
Area of triangle = 1/2 × 12 × 3
Area of triangle = 36/3
Area of triangle = 18 units
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(37) + (-2) + (-65) + (-8)
You have the following expression:
(37) + (-2) + (-65) + (-8)
eliminate parenthesis with the required change of signs:
37 - 2 - 65 - 8
sum negative numbers
37 - 75
simplify: rest the numbers and put the sign of the higher number:
-38
Then, you have:
(37) + (-2) + (-65) + (-8) = -38
how to solve the problem “Compute 3'7 mod 7”
Given
[tex]3^7mod\text{ }7[/tex]Find
Compute the value of mod
Explanation
We have given
[tex]3^7mod\text{ }7[/tex]as we can rewrite it
[tex]\begin{gathered} 3^7mod\text{ 7} \\ 2187mod7 \\ \end{gathered}[/tex]here , we see dividend , a = 2187 and divisor , b = 7
we know ,
[tex]a\text{ mod b = a- \lparen int \lparen a/b\rparen}\times b\text{\rparen}[/tex]where int is a integer part of the value .
so ,
2187 mod 7 = 2187 -(Int (2187/7)*7)
2187 mod 7 = 2187 - 312 *7
2187 mod 7 = 2187 - 2184
2187 mod 7 = 3
Final Answer
Therefore , the value of 3^7 mod 7 = 3
Christina made 4 three-point shots and 5 two-point shots in her basketball game. How many points (p) did she score?
The total points Christina made is as follows:
[tex]T=4\cdot3+5\cdot2=12+10=22[/tex]Then, Christina scored 22 points.
If f(x) = 5x + 40, what is f(x) when x = -5?
we have the following:
[tex]f\mleft(x\mright)=5x+40[/tex]replacing, x = -5
[tex]\begin{gathered} f(-5)=5\cdot-5+40 \\ =-25+40 \\ =15 \end{gathered}[/tex]The answer is 15
Explain how you can use an array to find partial products for 4x36.
Answer:
(4 x 30) +(4 x6)
120 + 24
144
Step-by-step explanation:
Ratios equivalent to 13:14
Equivalent fractions are those that, despite their visual differences, reflect the same value. For instance, if you take a cake and cut it into two equal pieces, you will have consumed half of the cake.
How can one determine equivalent fractions?When two fractions are expressed in their simplest form, they are said to be equivalent. When broken down into its simplest components, the fraction 26/28 equals 13/14. You only need to multiply the numerator and denominator of the reduced fraction (13/14) by the same natural number, i.e., multiply by 2, 3, 4, 5, 6 to get analogous fractions.
13 and 14 in decimal form.In decimal form, 13/14 is 0.92857142857143.
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Solve this inequality for the y variable: 6x-9y> 12 u y GON 4 3 2 4 O ya 3 2. 4 ys vs - 2 x + 2
We solve the inequality as follows:
[tex]6x-9y>12\Rightarrow-9y>-6x+12[/tex][tex]\Rightarrow y<\frac{2}{3}x-\frac{4}{3}[/tex]I need help please 5. Find the distance between C (-5, 4) and Q (2,0). A. 22 B. 33 C. 53 D. 65
Given the two points:
C (-5, 4) and Q (2, 0)
To find the distance, use the distance formula below:
[tex]d\text{ =}\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where,
(x1, y1) = (-5, 4)
(x2, y2) = (2, 0)
Therefore, we have:
[tex]\begin{gathered} d=\sqrt[]{(2-(-5))^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{(2+5)^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{7^2+(-4)^2} \\ \\ \text{ =}\sqrt[]{49+16} \\ \\ \text{ =}\sqrt[]{65} \end{gathered}[/tex][tex]undefined[/tex]you and three friends share a sushi boat at House of Kobe the cost of the boat is $50 you each also pay for a soft drink that is $2.39 what is the total cost of the meal after you pay 6% tax
ANSWER
$63.13
EXPLANATION
We have that the cost of the boat is $50.
Each of you and your friends (that is four of you) will pay for a soft drink that cost $2.39 each.
The cost of the soft drinks will therefore be:
4 * 2.39 = $9.56
Adding the cost of the boat, total cost will be:
$9.56 + $50 = $59.56
Now, we have to add a tax of 6%, so we find 6% of total cost:
[tex]\frac{6}{100}\cdot\text{ 59.56 = \$3.57}[/tex]Finally, add the tax to the cost:
$59.56 + $3.57
= $63.13
You pay a total of $63.13 (including tax)
An oil slick is expanding as a circle. The radius of the circle is currently 2 inches and is increasing at a rate of 5 inches per hour. Express the area of the circle, as a function of ℎ, the number of hours elapsed. ( Answer should be (ℎ)= some function of ℎ, enter as pi )
Answer: f(h) = (2 pi (5x + 2)^2)
Step-by-step explanation:
1) Set the area of the circle in an equation
f(h) = pi r ^2
2) Set r to the rate that the circle is growing
The rate is 5x +2 because its starting value is two, and the 5x because it is growing 5 inches per hour.
f(h) = (2 pi (5x + 2)^2)
An item is regularly priced at $50. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?Amount discounted: sX5?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
regular price = $50
discount = 40% = 0.4
Step 02:
amount discounted:
amount discounted = regular price * discount
amount discounted = $50 * 0.4 = $20
The answer is:
$20
Which fraction is the smallest?8/9, 9/10, 11/12, 12/13
Given:
[tex]\frac{8}{9},\frac{9}{10},\frac{11}{12},\frac{12}{13}[/tex][tex]\frac{8}{9}=0.8889[/tex][tex]\frac{9}{10}=0.9[/tex][tex]\frac{11}{12}=0.9167[/tex][tex]\frac{12}{13}=0.9231[/tex][tex]\frac{8}{9}\text{ is the smallest fraction.}[/tex]PLEASE HELP ME PLEASE I WILL GET A 0 ON THIS PLEASE HELP PLEASE
Answer:
[tex]58.29[/tex] cm
Step-by-step explanation:
So the area of a trapezium follows this equation/formula: [tex]\frac{a+b}{2} h[/tex]
So we pretty much just substitute the numbers given into this equation
[tex]\frac{a+b}{2} h[/tex]
[tex](\frac{7+10.4}{2} )6.7[/tex]
[tex](\frac{17.4}{2} )6.7[/tex]
[tex](8.7) 6.7[/tex]
[tex]58.29[/tex] cm
The sum is the measure of three angles of a triangle is 180 degrees. In a triangle, the measures of an angle are x,x+12 and x-48. What is the measure of each angle?
Answer:
24° , 72° , 84°
Step-by-step explanation:
sum the 3 angles and equate to 180 , that is
x + x + 12 + x - 48 = 180
3x - 36 = 180 ( add 36 to both sides )
3x = 216 ( divide both sides by 3 )
x = 72
Then the measure of the 3 angles are
x = 72°
x + 12 = 72 + 12 = 84°
x - 48 = 72 - 48 = 24°
A table is on sale for 38% off. The sale price is $527.00.What is the regular price?
Given:
A table is on sale for 38% off, The sale price of table is $527.00.
To find:
The regular price of the table.
Step by step solution:
To solve this problem, we need to use the basic formula of sales price and discount:
Sale price = $527.00
Discount percentage= 38%
[tex]\begin{gathered} \text{sale price = cost price - discount }\times\text{ \lparen cost price \rparen} \\ \\ 527=cp-\frac{38}{100}(cp) \\ \\ 527=\frac{62}{100}(cp) \\ \\ cp=\frac{52,700}{62} \\ \\ cp=850 \end{gathered}[/tex]From here we can say that the Cost-price / Regular price of the table is equal to $850.
help meeeeeee pleaseee !!!!
The linear function that passes through the two points (-6, -2) and (-9, -1) is defined by the rule:
y = -(1/3)*x - 4
How to find the linear function with the given points?The general linear function in the slope-intercept form:
y = m*x + k
Where m is the slope (also called rate of change) and k is the intercept of the y-axis.
If we know that the line passes through two points (a, b) and (c, d) then the slope of the function is:
m = (d - b)/(c - a)
So with only two points, we can find the slope.
In this case, the line passes through the points (-6, -2) and (-9, -1) , then the slope is:
m = (-1 +2)/(-9 + 6) = 1/-3 = -1/3
Then the slope is m = -1/3
So the linear function is something like:
y = (-1/3)*x + k
To find the value of k i will use the pint (-9, -1), replacing these values we get:
-1 = -(1/3)*-9 + k
-1 = 3 + k
-1 - 3 = k
-4 = k
So the linear function that passes through these points is:
y = -(1/3)*x - 4
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After how many months of saving do Sam and Frank have thesame amount in their accounts? How much do they have in theiraccounts at this time? Use the graph to explain your answer.
Answer:
To find: After how many months of saving do Sam and Frank have the same amount in their accounts and how much do they have in their accounts at this time
From the graph,
x axis represents number of months,
axis represents Amount saved.
The red graph represents the amount saved by Sam over the number of months
The blue graph represents the amount saved by Frank over the number of months
To find the intersection point of the two graphs.
The intersection point is (4,80)
After 4 months Sam and Frank saved $80.
Hence we get that,
After 4 months, Sam and Frank have the same amount in their accounts. They have $80 in their accounts.
Answer is: After 4 months, Sam and Frank have the same amount in their accounts. They have $80 in their accounts.
3300 dollars is placed in an account with an annual interest rate of 6.75%. To
the nearest tenth of a year, how long will it take for the account value to reach
10700 dollars?
The simple interest formula is A = P(1+r t) then the value of t =33.2210 years.
What is meant by simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The simple interest formula is equal to
A = P(1+r t)
where, A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
P = $ 3300
A = $ 10700
r = 6.75 % = 6.75 / 100 = 0.0675
substitute in the formula above
$10700 = 3300(1+0.0675 t)
simplifying the above equation, we get
Divide both sides by 3300
[tex]$\frac{3300(1+0.0675 t)}{3300}=\frac{10700}{3300}$$[/tex]
Simplifying the above equation, we get
[tex]$1+0.0675 t=\frac{107}{33}$$[/tex]
Subtract 1 from both sides
[tex]$1+0.0675 t-1=\frac{107}{33}-1$$[/tex]
Simplifying the above equation, we get
[tex]$0.0675 t=\frac{74}{33}$$[/tex]
Divide both sides by 0.0675
[tex]$\frac{0.0675 t}{0.0675}=\frac{\frac{74}{33}}{0.0675}[/tex]
[tex]$t=\frac{74}{2.2275}$[/tex]
t = 33.2210 years
Therefore, the value of t exists 33.2210 years.
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P(6, -3); y = x + 2
Write an equation for the line in point-slope form.
The equation of the line by using slope value is: y = x -9
What is slope of a line?
The slope of a line explain the steepness of the line segment. It is ration of the coordinates of the y-axis and the vertical coordinates of the x-axis. Depending upon the slope value, it is classified as whether lines are parallel or perpendicular.
According to the question, the given parameters for the line segment is as written below:
Equation of a line = x + 2 and the coordinate points = (6, -3): (x = 6; y = -3)
Now, by using standard equation for the line segment: y = mx + c
where, 'm' is the slope; c is the y-intercept; (x, y) are coordinates
Substituting given values that is slope and y-intercept in the standard equation, we get:
y = mx + c
⇒ -3 = (1)(6) + c
⇒ c = -3 - 6 = -9
Therefore, the value of the y-intercept is: c = (-9)
equation of the line by substituting the value of the y-intercept as well as slope value:
y = (1)x + (-9) = y = x -9
Hence, the equation of the line by using slope value is: y = x -9
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Given the equation of a curve is y=5/x²The value of dy/dx= -10/27Hence, estimate the value of 5/(2.98)²
The given equation is:
[tex]y=\frac{5}{x^2}[/tex]a. Find the value of dy/dx when x=3
Start by finding the derivative:
[tex]\frac{dy}{dx}=\frac{d(\frac{5}{x^2})}{dx}[/tex]You also can express 5/x^2 as 5*x^(-2):
[tex]\frac{5}{x^2}=5x^{-2}[/tex]You know the derivative of a power is:
[tex]\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]Apply it to your case:
[tex]\frac{d}{dx}5x^{-2}=(-2)\cdot5\cdot x^{-2-1}=-10\cdot x^{-3}[/tex]And finally:
[tex]\begin{gathered} x^{-n}=\frac{1}{x^n} \\ \text{Apply it to your equation} \\ \frac{dy}{dx}=\frac{-10}{x^3} \end{gathered}[/tex][tex]\begin{gathered} \text{When x=3} \\ \frac{dy}{dx}=\frac{-10}{3^3}=\frac{-10}{27} \end{gathered}[/tex]b. Estimate the value of 5/(2.98)^2:
[tex]\begin{gathered} y=\frac{5}{x^2}=\frac{5}{2.98^2}=0.563 \\ \text{Which also means x=2.98} \\ \text{Let's find the derivative when x=2.98} \\ \frac{dy}{dx}=\frac{-10}{2.98^3}=\frac{-10}{26.46}=-0.377 \end{gathered}[/tex]The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:98.9 96.6 98.6 99.7 97 97.4 99.4Assume body temperatures of adults are normally distributed. Based on this data, find the 98% confidenceinterval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e.,parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.98% C.I. -
Given the data temperatures to be;
[tex]98.9,96.6,98.6,99.7,97,97.4,99.4[/tex]We would require the following to get the 98% confidence interval of the mean body temperature.
Mean, Standard deviation, sample size, Probability of a confidence interval of 98%.
Using a calculator, we can get the mean to be
[tex]\text{(}\mu)=98.2285[/tex]The standard deviation would be derived to be;
[tex]\sigma=1.2230[/tex]The sample size can be gotten from the question to be;
[tex]n=7[/tex]The probability value of a 98% confidence interval is given to be 2.33
We can then derive the answer using the formula below;
[tex]\mu\pm z^x(\frac{\sigma}{\sqrt[]{n}})[/tex]We would substitute into the formula
[tex]\begin{gathered} \mu\pm z^x(\frac{\sigma}{\sqrt[]{n}}) \\ =98.2285+2.33(\frac{1.2230}{\sqrt[]{7}}) \\ =98.2285\pm1.0770 \\ =(97.152,99.306) \end{gathered}[/tex]ANSWER:
[tex](97.152,99.306)[/tex]1. The state of Ohio conducted COVID 19 tests on 68,811 people, and 8,533 tested positive. (6 points)A. What is p for the number who tested positive (round to the nearest hundredth of a percent)?B. Based upon the testing results above, of the 11.69 million people who live in Ohio, what is the bestestimate for the number of people who would test positive for the virus?
To find the probability for the number who tested positive we divide the positive cases between the total of the covid tests and then mutiply by 100.
P = (8,533/68,811)* 100
P = 12.400, the nearest hundredth of a percent is 12.
11690000 people who live in ohio and the testing results is that 12% of this people would test positive for the virus. so we need to find percentage 12 for 11690000.
(11690000* 12) / 100
1402800 is the number of people who would test positive for the virus
Please help me solve and show the steps so I could understand
Given polygon with sides 8 and radius 10yd.
Formula for area of ploygon
[tex]=n\times r^2\times tan\left(\frac{\pi}{n}\right)[/tex]So, solving further
[tex]\begin{gathered} =8\times10^2\times tan(\frac{\pi}{8}) \\ =800\times0.414 \\ =331.37 \end{gathered}[/tex]Hence, 331.37 yd square is the area of polygon.
Use a model to divide. 2/5÷4 Express the answer in simplest terms.
so the equation si:
[tex]\frac{\frac{2}{5}}{4}[/tex]This is equal to:
[tex]\frac{2}{20}=\frac{1}{10}[/tex]Finally:
[tex]\frac{1}{10}=0.1[/tex]Which equation is the correct translation of the following statement?Four less than a number is nine.9 - x = 49 - 4 = xx - 4 = 94 - x = 9
Given
The statement,
Four less than a number is nine.
To find:
Which equation is the correct translation of the following statement?
Explanation:
Let x be the number.
Since four less than a number is nine.
Then,
[tex]x-4=9[/tex]Hence, the correct statement is x-4=9.
A falling object travels a distance given by the formula d = 4t + 6t?, where d is measured in feet and t is measured in seconds.
How many seconds will it take for the object to travel 68 feet? Round the answer to 4 decimal places.
If a falling object travels a distance given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the time taken by the object to travel 68 feet is 3.0496 seconds
The formula of the object traveling a distance d = 4t + [tex]6t^{2}[/tex]
Where d is the distance traveled in feet
t is the time taken in seconds
Here
The distance traveled = 68 feet
Therefore the equation will be
68 = 4t + [tex]6t^{2}[/tex]
[tex]6t^{2} +4t-68=0[/tex]
We have to solve quadratic equation [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
a = 6
b = 4
c = -68
Substitute the values in the equation
= [tex]\frac{-4+/-\sqrt{4^2-(4)(6)(-68)} }{(2)(6)}[/tex]
= [tex]\frac{-4+/-\sqrt{1648} }{12}[/tex]
t = [tex]\frac{-1+/-\sqrt{103} }{3}[/tex]
We take only positive value
t = [tex]\frac{-1+\sqrt{103} }{3}[/tex]
t = 3.0496 seconds
Hence, if a falling object travels a distance given by the formula d = 4t + [tex]6t^{2}[/tex] where d is the measured in feet and t is measured in seconds, then the time taken by the object to travel 68 feet is 3.0496 seconds
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3,000 is 1/10 of?-30030,000300,000
Let X be the number, then we know that
[tex]\frac{X}{10}=3,000[/tex]If we isolate X by moving 10 to the right hand side, we obtain
[tex]\begin{gathered} X=10\cdot3,000 \\ X=30,000 \end{gathered}[/tex]that is, the answer is 30,000