Answer:
take square root on both side
Step-by-step explanation:
Three people travel by car to San Diego, a distance is 380 miles. Thetrip takes 6 hours. Daily cost for meals is $20 per person and gas costs$3.59 per gallon and their vehicle gets 15 mpg. Calculate the cost perperson for this trip to the nearest dollar.A) $85B) $70C) $50D) $90E) $105
Given:
• Distance = 380 miles
,• Time = 6 hours
,• Daily cost for meals = $20 per person
,• Cost of gas = $3.59 per gallon
,• Vehicle gets 15 miles per gallon.
Let's calculate the cost per person for this trip.
We have the following:
To find the total cost of gas they used for this trip, we have:
[tex]\frac{380}{15}*3.59=90.95[/tex]The total cost of gas for this trip is $90.95
The cost of gas per person will be:
[tex]\frac{90.95}{3}=\text{ \$30.32}[/tex]Cost of gas per person is $30.32
Therefore, the cost per person for this trip will be:
Cost per person = Cost of gas per person + Cost of meal per person
Cost per person = $30.32 + $20 = $50.32 ≈ $50
Therefore, the cost per person for this trip to the nearest dollar is $50
ANSWER:
C) $50
The Massive Chemical Corporation starts an annuity to pay for the huge government penalties they expect in 11 years when a pending case finally gets litigated.Their lead attorney informs them that they can expect a $4,000,000 fine. An investment house offers 11.5% interest on annuities of that size, compoundedsemiannually. What will the semiannual payment be on this annuity? Round to the nearest cent.
To solve this problem we can use the formula for compound interes so the equation is:
[tex]Y=P_o(1+I)^t[/tex]Kennedy's car used 16 gallons to travel 288 miles. How many miles can the car go for
each gallon of gas?
Answer:
18 miles
Step-by-step explanation:
The car needs 16 gallons to travel 288 miles. We can divide by 16, kind of like dividing on both sides of an equation, to get that with 1 gallon, the car can travel 288/16=18 miles.
for choose one you have to tell me what kind of angle it is.
Part 1
By angle addition property
m<4+m<5+m<1=180 degrees
m<4=39 degrees
m<5=45 degrees
substitute
39+45+m<1=180
m<1=180-39-45
m<1=96 degreesPart 2
we see that
m<4 and m<3 are alternate interior angles
and since lines, l and k are parallel, <4 and <3 are congruent
so
m<3=39 degreesPart 3
we see that <2 and <5 are alternate interior angles
and since lines, l and k are parallel, < 2 and <5 are congruent
so m<2=45 degrees
Part 4
therefore m<1+m<2+m<3=180 degrees
The relationship between <1, <2 and <3 is an example of the following rule
The sum of the interior angles measures of a triangle is 180 degrees
How to simplify the 6th root of y^21
The simplified expression is [tex]y^{\frac{7}{2} }[/tex]
How is the given expression simplified?
[tex]6\sqrt{y^{21} } \\\\= [(y)^{21} ]^{\frac{1}{6} } \\\\[/tex]
By applying power rule of exponents ,
[tex]6\sqrt{y^{21} } =[/tex] [tex]y^{\frac{7}{2} }[/tex]
What is power rule of exponents?
The exponent power rule is [tex](a^{m} )^{n} = a^{mn}[/tex]Exponent times power is how you raise a number with an exponent to a power.When a base is raised to a power and then the entire expression is raised to another power.An algebraic expression can be made simpler by using the power of a power rule in exponents.To learn more about power rule, refer:
https://brainly.com/question/819893
#SPJ9
The abbreviated form is
How is the expression that is given simplified?
by using the exponents' power rule.
What is the exponents power rule?
Exponent power rule states that
You increase a number with an exponent to a power by multiplying the exponent by the power.when the expression as a whole is raised to a higher power after raising a base to that powerThe power of a power rule in exponents can be used to simplify an algebraic expression.To learn more about power rule refer to:
brainly.com/question/819893
#SPJ9
PLEASE HELP FOR 20 POINT! The area model shows 3 and one-fourth. What is 3 times 3 and one-fourth?
An area model has 4 shaded rectangles. An area model has 4 shaded rectangles. An area model has 4 shaded rectangles .An area model has 1 shaded rectangle and 3 unshaded rectangles.
3 and one-fourth
3 and three-fourths
9 and one-fourth
9 and three-fourths
The multiplication of the mixed number 3 1/4 by 3 has a result given as follows:
9 and three-fourths.
Mixed numbersA mixed number is modeled as follows:
a b/c.
In which the integer and the fractional parts are given as follows:
a is the integer part of the number.b/c is the fractional part of the number.To apply multiplication involving mixed numbers, we convert these numbers to fractions, as follows:
a b/c = (ac + b)/c
In this problem, the mixed number is given as follows:
3 1/4.
Hence the fraction is given as follows:
(3 x 4 + 1)/4 = 13/4
The multiplication by 3 is given as follows:
3 x 13/4 = 39/4.
The division of 39 by 4 has a quotient of 9 and a remainder of 3, hence the mixed number that represents the division is:
9 and three-fourths.
Learn more about mixed numbers at brainly.com/question/21610929
#SPJ1
Two rows of fluorescent lamps are installed in an office on the same branch circuit, with each row drawing 12.5 amperes. The source voltage is 277 volts, and the line resistance is 0.5 Ω. The wire used has a constant (k) of 12.6. The voltage drop will be within the recommendation of the NEC.
what number do I need to add -5 to get -7
- 5 - 2 = - 7
The number that you need to add to - 5 to get - 7 is - 2
This can be ssen on the number line. If you are adding, you move towards the right but since we are adding a negative number, the - sign makes the plus sign to become - sign. So we would subtract by moving 2 points to the left of -5 and that gives - 7
What is the perimeter of STUV?* STUV – XYZW T Z 20
The perimeter of the figure is the addition of the segments so in this case we have to find the sides so:
[tex]\frac{35}{21}=\frac{25}{TU}=\frac{20}{UV}=\frac{20}{SV}[/tex]So:
[tex]\begin{gathered} TU=\frac{25\cdot21}{35}=15 \\ UV=\frac{20\cdot21}{35}=12 \\ SV=\frac{20\cdot21}{35}=12 \end{gathered}[/tex]So the perimeter will be:
[tex]\begin{gathered} P=21+15+12+12 \\ P=60 \end{gathered}[/tex]Write this equation in Y=MX+B form: 3x+4y=8
the initial expression is:
[tex]3x+4y=8[/tex]So to write it in the form slope intercept we can rest 3x in bout sides of the equation so:
[tex]\begin{gathered} -3x+3x+4y=-3x+8 \\ 4y=-3x+8 \end{gathered}[/tex]now we divide by 4 so:
[tex]\begin{gathered} \frac{4y}{4}=-\frac{3}{4}x+\frac{8}{4} \\ y=-\frac{3}{4}x+2 \end{gathered}[/tex]No M is equal to -3/4 and B is equal to 2e
Answer:
y = -3/4x + 2
Step-by-step explanation:
Given:
Write this equation in "y=mx+b form"
Equation given: 3x+4y=8
Solve:
3x + 4y = 8
⇒ 3x -3x + 4y = 8 -3x ⊂ Subtract 3x from both side ⊃
⇒ 4y = -3x + 8
⇒ 4y/4 = -3x/4 +8/4 ⊂ Divide all by 4 ⊃
⇒ y = -3/4x + 2
Hence, this equation ( 3x + 4y = 8) in y = mx+b is y = -3/4x + 2
Lenvy~♡
Find the area swept by the door. Note: Enter your answer in terms of \piπpi.
We are asked to determine the area swept by the door. We notice that the area forms a sector of a circle. The area of the sector of a circle is given by:
[tex]A=\frac{1}{2}r^2\theta[/tex]Where:
[tex]\begin{gathered} A=\text{ area} \\ r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}[/tex]To convert the given angle into radians we use the following conversion factor:
[tex]\pi\text{ radians = 180 degr}ees[/tex]Now, we multiply by the conversion factor:
[tex]45\times\frac{\pi}{180}=\frac{\pi}{4}[/tex]Now, we plug in the values in the formula for the area:
[tex]A=\frac{1}{2}(80cm)^2(\frac{\pi}{4})[/tex]Solving the operations:
[tex]A=800\pi cm^2[/tex]Therefore, the area is 800 pi square centimeters.
TWO tailors, Aisha and Debbie, sit down to do some embroidery. Alsha can embroider 4 shirtsper hour, and Debbie can get through 6 shirts per hour. In addition, the tailors had previouslyfinished some shirts. Aisha has already completed 20 shirts, and Debbie has completed 10shirts. Aisha and Debbie decide to take a break when they have finished the same totalnumber of shirts. How long will that take?Write a system of equations, graph them, and type the solution
For the information given in the statement you have
[tex]\begin{gathered} t=4h+20\Rightarrow\text{ shirts embroidered by Aisha} \\ t=6h+10\Rightarrow\text{ shirts embroidered by Debbie} \end{gathered}[/tex]Find an equation for the line that bisects QII and QIV. Write your answer in general form.
Consider the equation y= mx+b
he line bisects two Quadrants II and IV,It passes through the origin.
the y intercept is =0
thus, the equation will be y=x
but the line is from the II to IV quadrants
the equation is y=-x.
What is the volume of a cone with height of 80 km and diameter 21 km?
The volume of a cone with height of 80 km and diameter 21 km is 9240km³.
How to determine the volume of a cone?Volume of a cone=R^2H/3
Diameter=21
To get the radius is half of diameter,:
Radius(R)= Diameter/2= 21/2=10.5kM
Height=80km
Volume=22/7×10.5^2×80/3
The volume of the Cone= 9240km^3
Read more about Cone
https://brainly.com/question/29224025
#SPJ1
A pharmaceutical company makes the capsule below. Find the volume of the capsule
the circumference of the circle is 76 cm. what is the area? using 3.14 for pi round to the nearest square cm
The circumference of a circle is gotten using the formula below;
[tex]\begin{gathered} C=2\pi r \\ \text{Where r is the radius of the circle} \end{gathered}[/tex]Step 1: Let's find the value of the radius;
[tex]\begin{gathered} C=2\pi r \\ r=\frac{C}{2\pi} \\ r=\frac{76}{2\times3.14} \\ r=\frac{76}{6.28} \\ r=12.10\operatorname{cm} \end{gathered}[/tex]Step 2: The area of the circle is given as;
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius of the circle} \\ A=3.14\times(12.10)^2 \\ A=459.73 \\ A=460\operatorname{cm}^2 \end{gathered}[/tex]Hence, the area of the circle is 460 square centimeters.
prove that the sum of the lengths of the diagonals of a quadrilateral is less than the perimeter but greater than the half of the perimeter of this quadrilateral
Let us consider a quadrilateral ABCD (as shown in the figure below) such that AC and BD are the two diagonals of ABCD.
Now, in triangle ABC and triangle ADC, by using the properties of triangle inequality we have-
AB +BC > AC .... (1)
and AD + CD >AC .... (2)
adding equations (1) and (2) we get-
AB+ BC+CD+AD > 2AC .... (3)
Similarly for diagonal BD we get-
AB+BC+CD+AD > 2BD .... (4)
Adding equations (3) and (4) we get-
2(AB+BC+CD+AD) > 2(AC+BD)
⇒ (AB+BC+CD+AD) > AC+BD
here (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence, we have proven that the sum of the length of the diagonals of a quadrilateral is less than the perimeter.
Now the 2 diagonals divide the quadrilateral into 4 quadrilaterals
Therefore, AO+OD > AD
OD+OC > CD
OC+OB > BC
and OA+OB > AB
Adding all these equations-
2(AC+BD)>AB+BC+CD+AD
⇒AC+BD > 1/2(AB+BC+CD+AD)
Hence, we've proven that the sum of the length of the diagonals is greater than the half of the perimeter of this quadrilateral.
Learn more about quadrilaterals here-
https://brainly.com/question/26690979
#SPJ1
A pizza parlor offers a choice of 12 different toppings. How many 2-topping pizzas are possible? (no double-orders of toppings are allowed)
==========================================================
Explanation:
There are 12 choices for the first topping and 11 for the next topping. The decrease is to account for the fact we cannot select a repeat topping.
That gives 12*11 = 132 permutations. If order of toppings mattered, then this would be our final answer.
However, the topping order doesn't matter. So we need to divide by 2 to correct for the double counting.
There are 132/2 = 66 combinations.
------------
Alternative Method:
n = 12 toppings are available and r = 2 selections are allowed
Order doesn't matter so we use the nCr combination formula
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\12 C 2 = \frac{12!}{2!*(12-2)!}\\\\12 C 2 = \frac{12!}{2!*10!}\\\\12 C 2 = \frac{12*11*10!}{2!*10!}\\\\ 12 C 2 = \frac{12*11}{2!}\\\\ 12 C 2 = \frac{12*11}{2*1}\\\\ 12 C 2 = \frac{132}{2}\\\\ 12 C 2 = 66\\\\[/tex]
There are 66 combinations
Notice the 2nd to last step involves 132/2 which was mentioned in the previous section.
Farmer Anders' pumpkin patch is shown below.
19 yards ,
11 yards ,
48 yards and
22 yards.
He purchases fertilizer that costs $2.68 per square foot of coverage, but he has a coupon for half off.
How much will he spent to apply fertilizer to the entire patch.
Please help me answer!
If the cost of fertilizer is $2.68 per square foot of coverage then the farmer need to spend an amount of $5085.3 to apply fertilizer to the entire patch.
Given that the farmer Anders' pumpkin patches are such that they are in rectangle and the lengths are 19 yards and 48 yards and the breadths are 11 yards and 22 yards.
We are required to find the amount of money that the farmer need to spend to apply the fertilizer to the entire patch.
Area which is covering the entire patch=11*19+22*48
=209+1056
=1265 square yards
We know that 1 yard=3 foot
Area in foot=1265*3
=3795 square foot
Amount for fertilizer=3795*3
=$10170.6
Since 1/2 is off so it will be $5085.3 ($10170.6/2).
Hence if the cost of fertilizer is $2.68 per square foot of coverage then the farmer need to spend $5085.3 to apply fertilizer to the entire patch.
Learn more about area at https://brainly.com/question/25292087
#SPJ1
The prism below is made of cubes which measure 3 of a centimeter on one side. What is the volume? NORSKEREN OA. LICO cubic cm OB. 8 cubic cm oc. i cubic cm 8 OD cubic cm 27
Recall that for a cube of this form
where the side is of length a, then the volume is calculated by the expression
[tex]a^3[/tex]So, to define the volume of the given cube, we should calculate the side's length of the bigger cube, based on the small cube
If we take a look at the front side of the cube we would look something like this
So, we want to determine the length's side of this square. We can see that in this case the length side corresponds to adding twice the length of one of the small cube. So the side's length of the new cube is
[tex]\frac{1}{3}+\frac{1}{3}=\frac{2}{3}[/tex]So, the volume of the bigger cube is
[tex](\frac{2}{3})^3^{}=\frac{2^3}{3^3}=\frac{8}{27}[/tex]So the volume of the bigger cube is 8/27 cubic centimeters
Kristen gets a full scoop of frozen yogurt in a cone. The scoop is aperfect sphere with the same radius as the cone. She wonders if theentire volume of the frozen yogurt could fit completely inside thecone. What is the relationship between the volume of the coneand the volume of frozen yogurt? Is the volume of the cone greatenough to fit all of the frozen yogurt? Explain. (Use 3.14 for (pie) andround your answer to the nearest whole number)
The volume of a sphere is calculated as follows:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius of the sphere.
Substituting with r = 5 cm, we get:
[tex]\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot5^3 \\ V=\frac{4}{3}\cdot\pi\cdot125 \\ V=523.3\operatorname{cm}^3 \end{gathered}[/tex]The volume of a right circular cone is calculated as follows:
[tex]V=\pi r^2\frac{h}{3}[/tex]where h is the height of the cone.
Substituting with r = 5 cm, and h = 11 cm, we get:
[tex]\begin{gathered} V=\pi\cdot5^2\cdot\frac{11}{3} \\ V=\pi\cdot25\cdot\frac{11}{3} \\ V=287.8\operatorname{cm}^3 \end{gathered}[/tex]The volume of the cone is less than the volume of the sphere, then the
entire volume of the frozen yogurt cannot fit completely inside the
cone.
I don’t know how to do 4 - 6mod6
Modulus (mod) symbol is a symbol that is used to find the remainder of the quotient of two integers
6mod6 means we need to find the result of the remainder if 6 is divided by 6.
Take the ratio of the integers
6/6 = 1.0
Multiply the result by the denominator
1.0 * 6 = 6
Take the difference of the result and the denominator
Remainder = 6 - 6
Remainder = 0
This shows that 6mod6 = 0
Substitute into the original expression
[tex]4-6mod6=4-0=4[/tex]Which of the following values are solutions to th I. 2 II. – 6 None O I only Submit Ang O II only O III only I and II I and III O II and III I, II and III
ok, but the inequality is not complete in the picture
[tex]\begin{gathered} \text{ 1 }\leq\text{ 1 - 2x} \\ \text{ 1 - 1 }\leq\text{ -2x} \\ \text{ 0 }\leq\text{ -2x} \\ \text{ 0/-2 }\ge\text{x} \\ \text{ 0 }\ge\text{ x} \end{gathered}[/tex]Identify all the sets to which the number belongs. Choose from rational number, irrational number, whole number, and itenger. 0.62478916532
0.62478916532 is an irrational number
This is because it cannot be expressed as a rational number except in surd form which is also known to be irrational. it is neither a whole number nor an integer too
ANSWER => Option B
A jellybean company produces 1,680 jellybeans per second. One box of jellybeans contains 50 jellybeans. What is this company’s production rate, in boxes of jellybeans per minute?
Answer:
2016
Step-by-step explanation:
1680:50=33.6
33.6x60=2016
Solve using the quadratic formula
To "double" a number means to multiply by two. It is often useful to be able to estimate the double of a number using mental math (without a calculator).
For example, a shirt costs $59. Estimate the cost to buy 2 shirts (disregard the tax).
Double the number $59 is $118 after applying the mental math, the answer is $118.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that:
To "double" a number means to multiply by two.
From the definition of the arithmetic operation, the operation in which we do the addition of numbers, subtraction, multiplication, and division.
Using mental math it can be easy to determine the double a number.
The number is $59
To double:
= 59 + 59
= 50 + 9 + 50 + 9
= 100 + 18
= $118
Thus, double the number $59 is $118 after applying the mental math, the answer is $118.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ1
A jewelry store sells a necklace at $365 that was original purchased at $240, what is the markup? Round your answer to the nearest whole percent.
We are given a selling price of $365 and a purchase cost of $240, we are asked to find the markup. The formula for calculating the mark up is the following:
[tex]\text{markup}=\frac{sale\text{ price-cost}}{\cos t}[/tex]we have that the sale price is 365 and the cost is 240. Replacing in the formula:
[tex]\text{markup}=\frac{365-240}{240}[/tex]solving the operations we get:
[tex]\text{markup}=\frac{125}{240}=0.52[/tex]This can be expressed as a percentage like this:
[tex]\text{markup}=52\text{ percent}[/tex]the markup is 52%
On a number line, the coordinates of X, Y, Z, and W are -7, -3, 1, and 5, respectively. Find the lengths of the two segments below. Then tell whether they are congruentXY and ZWThe length of XY isThe length of ZW is(Type an integer or a decimal.)(Type an integer or a decimal.)
The Solution:
Given:
[tex]\begin{gathered} X=-7 \\ Y=-3 \\ Z=1 \\ W=5 \end{gathered}[/tex]Required:
Determine whether segment XY is congruent to segment ZW.
Step 1:
Find the length of segment XY.
[tex]XY=-3-(-7)=-3+7=4[/tex]Step 2:
Find the length of segment ZW.
[tex]ZW=5-1=4[/tex]Since:
[tex]\begin{gathered} XY=ZW=4 \\ It\text{ follows that XTY and ZW are congruent.} \end{gathered}[/tex]Answer:
XY = 4
ZW = 4
They are congruent.
do you think you'd be able to help me out here
1) Let's make a graph for that round trip with stops.
2) Continuing the graph, on the way back
Considering that every time the plane stops, its altitude goes down to 0, i.e. a point in the x-axis, then we can count 4 stops, 1 in the Chicago-NY and 3 on the way back. Considering that the graph touches the x-axis when it lands then the graph touches 6 times
