The Bus can hold 59 students and van can hold 18 students.
How to illustrate the equation?The freshman class rented and filled 1 van and 6 buses with 372 students. This can be illustrated as:
v + 6b = 372 .... i
The sophomore class rented and filled 4 vans and 12 buses with 780 students. This can be illustrated as:
4v + 12b = 780 ... ii
where v = van.
b = bus
v + 6b = 372
4v + 12b = 780
Reduce equation ii by 2. The new equations will be:
v + 6b = 372
2v + 6b = 390
Subtract
v = 18
The van can hold 18 students
Since v + 6b = 372
This will be:
18 + 6b = 372
6b = 354
b = 59.
Bus can hold 59 students.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75. If the
manager spent a total of $38.50, how many pens did the store manager purchase?
The number of pens the store manager purchase, if A store manager purchased a total of 15 pens and markers, is 7.
What is the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75, the manager spent a total of $38.50,
Write the equation of the statement as shown below,
x + y = 15 and 3.5x + 1.75y = 38.5
Here, x is the number of pens and y is the number of markers,
Solve the equations by using the elimination method,
x = 7, y = 15 - 7 = 5
To know more about equation:
https://brainly.com/question/12788590
#SPJ1
Point M is the midpoint of PQ , and LM is the perpendicular bisector of PQ . Write a two-column proof to show that LP=LQ .
The two-column proof shows that LP = LQ
LP = √(LM² + PM²)
LQ² = √(LM² + PM²)
LP = LQ
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Point M is the midpoint of PQ.
This means,
PM = QM ______(A)
LM is the perpendicular bisector of PQ .
L
/ | \
/ | \
/ | \
P M Q
Applying the Pythagorean theorem.
Triangle LMP is a right triangle.
LP = LM² + PM² _____(1)
Triangle LMQ is a right triangle.
LQ² = LM² + QM² _____(2)
Thus,
From (A), (1), and (2) we get,
LP = √(LM² + PM²)
LQ² = √(LM² + PM²)
LP = LQ
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ1
Logarithms and natural logarithms are fundamentally different math structures and rely on totally different sets of properties to worth with.
True or False
Given: triangle ABC is congruent to triangle ADC
Prove: AC bisects angle BAD and AC bisects angle BCD
Please help and thanks if you do
AC bisects angle BAD and AC bisects angle BCD is proved using CPCT rule.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, ΔABC≅ΔADC.
We know that, corresponding parts of congruent triangle are equal.
So, ∠BAC=∠DAC (∵CPCT)
∠BCA=∠DCA (∵CPCT)
∠BAD=∠BAC+∠DAC
⇒ ∠BAD=2∠BAC
⇒ ∠BAC=∠BAD/2
So, AC bisects ∠BAD
∠BCD=∠BCA+∠DCA
⇒ ∠BCD=2∠BCA
⇒ ∠BCD/2=∠BCA
So, AC bisects ∠BCD
Hence, proved AC bisects ∠BAD and AC bisects ∠BCD.
To learn more about the congruent theorem visit:
https://brainly.com/question/24033497.
#SPJ1
how many eight digit numbers contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes? leading 0s are allowed.
0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.
According to collect from the data
Let us assume that the data as followed by
How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.
Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.
2,3,3,4,4,4
now then:
= 8!/2!3!3!4!4!4!
= 8.7.6.5.4!/2×6×6×24×24×4!
= 35/864
Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .
Learn more about Permutations and combinations here:
brainly.com/question/4658834
#SPJ4
How do you find the equation of a line with 2 lines?
By entering the values of m and b into the slope-intercept form of a line (y = mx + b), you may obtain the equation for the line.
Given,
Equation of a line;
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
We have to find the equation of a line with 2 points;
Here,
Using the slope formula, determine the slope.Slope, m = (y₂ - y₁) / (x₂ - x₁)
To find the y-intercept, use the slope and one of the points (b).The x and y of your equation y = mx + b can be replaced by one of your points, and the m can be replaced by the slope you just calculated. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.
Therefore,
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx + b).
Learn more about equation of line here;
https://brainly.com/question/259557
#SPJ4
What is the radius of a circle whose equation is x2 y2 8x â 6y?
The radius of a circle with equation is x² + y² + 8x - 6y + 21 = 0 is 2 units .
In the question ,
it is given that ,
the equation of circle is ⇒ x² + y² + 8x - 6y + 21 = 0 ,
we know that the general equation of the circle is x²+y²+2fx+2gy+c=0
so , the radius of the circle is calculated using the formula ,
radius = √(f² + g² - c)
On comparing the given equation with general equation
we get , the values of f as 4 and g as -3 .
So after substituting the values of f , g and c in the radius formula ,
we get ,
radius = √(16 + 9 - 21)
= √(16 + 9 - 21)
= √(25 - 21)
= √(4) = 2 .
Therefore , the radius of given circle is 2 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 ?
Learn more about Circles here
https://brainly.com/question/5720980
#SPJ4
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 440 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.
The equations that could be used to determine the number of small boxes sent and the number of large boxes sent is 85b = 440.
What is the system of equations that could be used to determine the number of small boxes sent and the number of large boxes?From the information, each small box can hold 20 books and each large box can hold 45 books.
There was also twice as many large boxes sent as small boxes, which altogether can hold 440 books.
This will be:
2(20b) + 45b = 440
where b = number of books
40b + 45b = 440
85b = 440
The equation is 85b = 440
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Christy Peterson's total income last year was $77,340. Of that amount, she spent $7,240 on transportation costs and $2,100 on clothing. What
percent of Christy's total income did she spend on transportation and clothing combined? Round your answer to the nearest percent.
Answer:
12%
Step-by-step explanation:
Christy Peterson's total income last year was $77,340. Of that amount, she spent $7,240 on transportation costs and $2,100 on clothing. What percent of Christy's total income did she spend on transportation and clothing combined? Round your answer to the nearest percent.
7,240 + 2,100 = $9,340
9,340 / 77,340 = 0.120765
0.120765 * 100 = 12.0765%
rounded = 12%
find a scalar equation of the plane that contains the point (1,2,3) and contains the line represented by the vector equation r(t)
The scalar equation of the plane that contains given points and lines can be written as: (-4)(x-1) + 4(y-2) + (-10)(z-3) = 0.
What is equation of plane?
A given point p(x, y, z) that is located on the plane and a normal vector n define the equation of a plane. A plane's vector and scalar components can be used to formulate the equation for the plane.
The parametric form of line equation,
[tex]p = p_0 + t. \vec v[/tex]
On comparing with the given equation in question, we can say that,
p = {x, y, z}, p₀ = {0, 6, 1,}, vec(v) = {3, -2, -2}
The scalar equation can be given by,
[tex][ \vec \omega, p - p_1] = 0[/tex]
Here, p₁ = {1, 2, 3} and ω is perpendicular to v and to the segment p₁ - p₀ So,
[tex]\vec \omega = \vec v \times (p_1 - p_0) = ( 3, -2, -2 ) \times (1, -4, -2)[/tex]
then,
[tex]\vec \omega = (-4, 4, -10)[/tex]
Therefore, the scalar equation can be written as:
(-4)(x-1) + 4(y-2) + (-10)(z-3) = 0
It can also be written as:
26 - 4x + 4y - 10z = 0
To know more about equation of line, go to link
https://brainly.com/question/10524369
#SPJ4
Complete Question
Find a scalar equation of the plane that contains the point (1,2,3) and contains the line represented by the vector equation r(t) = [3t, 6 - 2t, 1 -2t] ?
Which is the graph of y = [x] -2?
make this in to an Inequality You have some money (m) and you want to bye snacks but your mom told you to also bye a pizza that cost $8. So on snacks you can spend.(s) s
Answer:
To turn the given statement into an inequality, we can write it in the form "m - s >= 8", which means that the amount of money you have (m) minus the amount you spend on snacks (s) must be greater than or equal to 8. This inequality represents the constraint that your mom has placed on your spending, requiring you to spend at least $8 on the pizza. In mathematical notation, the inequality would be written as:
m - s >= 8
This inequality states that the amount of money you have, minus the amount you spend on snacks, must be greater than or equal to 8 in order for you to be able to buy the pizza.
Step-by-step explanation:
FIRST PERSON GETS BRAINLIEST! Identify the measure of angle x
Answer:
Step-by-step explanation:
180=28+73+x
180-28-73=79
79=x
What is the point-slope form of the line with slope − 14 that passes through the point − 2 9 )?
y - 9 = -14(x + 2) is the point-slope form of the line with slope − 14 that passes through the point − 2 9 )
Given a line with slope -14 that passes through the point (-2, 9).
To determine the point-slope form of the line, we need to use the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values into the formula, we get:
y - 9 = -14(x + 2)
Therefore, the point-slope form of the line is y - 9 = -14(x + 2).
Learn more about slope here
https://brainly.com/question/3605446
#SPJ4
a rectangle is bounded by the -axis and the semicircle (see figure). what length and width should the rectangle have so that its area is a maximum?
Length and width should the rectangle have so that its area is a maximum are 4.242 and 2.121 respectively.
From the question, we have
Area = A = xy
A = xsqr(9-x^2)
Taking the derivative and set = 0
A' = (x/sqr(9-x^2)(-2x) + sqr(9-x^2) = 0
A' = -x^2 + 9 -x^2 = 0
-2x^2 =-9
x^2 = 9/2
x = 3/sqr2 = (3/2)sqr2 = 4.242
y = sqr(9-x^2) = sqr(9-9/2) = 3sqr2/2 = 2.121
Dimensions of the rectangle are 4.242 and 2.121 respectively
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
Complete question:
A rectangle is bounded by the x-axis and the semicircle y = radical 9 − x^2 (see figure). What length and width should the rectangle have so that its area is a maximum?
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ4
Shen and Linda are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.
Answer:
a. shen's car
8 gallons
b. 400 miles
shen's car
horace horsecollar is interested in the opinion of vacationers at disney world. he creates a short survey and administers it to every 1000th person to enter the park, starting with the 364th person. what method did horace use to select his sample?
The method used by Horace to select his sample is Systematic Sampling.
A form of probability sampling technique called systematic sampling selects sample members from a broader population using a predetermined, periodic interval in addition to a random beginning point. The population size is divided by the intended sample size to arrive at this range, which is known as the sampling interval.
Horace desires to select every 1000th person to enter the park, starting with the 364th person. So he selects the 364th person, 1364th person, 2364th person, and so on. This is a perfect situation for Systematic Sampling.
To read more about Systematic Sampling, visit https://brainly.com/question/24317913
#SPJ4
A rectangular sheet of material has a width that is 6 cm less than its length. The area of the sheet of material is 72 cm². What must be the width of the rectangular sheet?
O 6 cm
O 8 cm
O 12 cm
O 16 cm
Answer:
width = 6 cm
Step-by-step explanation:
Area = width x length
let x = length
width = x - 6
A = 72 cm² = x(x-6) = x² - 2x
rewrite the equation:
x² - 2x - 72 = 0
solve for x by factoring or the quadratic equation:
(x-12)(x+6) = 0
x = 12, -6
therefore x = length = 12
Width = 12 - 6 = 6
conduct the appropriate hypothesis test and compute the p-value. sunshine air has determined that their no-show rate for passengers booked on a flight is 6%. the airline has recently increased the cost of its travel insurance and and suspects the no-show rate for passengers will decrease. a random sample of 380 reservations resulted in 18 no-shows. at the 0.10 significance level, is there strong enough sample evidence to suggest that the no-show rate in less than 6%?
The p-value is 0.15 which is greater than the significance value 0.10 so null hypothesis cannot be rejected at 10% significance level , we do not have enough evidences to state that no- show rate is less than 6%.
As given in the question,
Null hypothesis : No show rate for passengers booked on given flight is 6%
Alternative hypothesis: No show rate for passengers booked on given flight is less than the 6%
P = 6%
= 0.06
1 - P = 1 - 0.06
= 0.94
random sample size 'n' = 380
no shows = 18
Sample proportion 'p' = 18/ 380
= 0.047
Now , z test statistic value :
z = (p - P)/ √P (1- P)/n
= (0.047 - 0.06)/√0.06( 0.94)/380
= -0.013 /0.012
= -1.083
p-value = 0.2788 ( using table)
0.2788 > 0.10
p-value is greater than significance value 0.10
Do not reject null hypothesis at 10% level of significance.
Therefore, as p-value is greater than significance value do not have enough evidences to state that no- show rate is less than 6%.
Learn more about p-value here
brainly.com/question/14790912
#SPJ4
What do we use SSS SAS ASA and AAS to prove?
The rules SSS SAS ASA and AAS are the rule that is used to prove the congruence of the triangle
The rules SSS SAS ASA and AAS are used to prove the congruence of the triangles .
The congruence means if shape and size of the one shape is same as the shape and size of the another shape, then we can say that both the shapes are congruent
If you consider the case of triangle, two triangle can be prove as congruent if the specifics sides and angles of the triangle is equal to the other triangles.
The rules that used to prove the congruence of the triangles are
SSS - side-side-side rule of congruence
SAS = side-angle-side rule of congruence
ASA = angle-side-angle rule of congruence
AAS = angle-angle-side rule of congruence
Therefore, these rules are used to prove the congruence of the triangle
Learn more about congruence rule here
brainly.com/question/29548914
#SPJ4
what is the slope of this line
Answer:
y = 300x + 100
Step-by-step explanation:
y = mx + c
the line intersects the y axis at 100, so c = 100
m = difference between y-coordinates / difference between x-coordinates
m = (400-100)/(1-0) = 300/1 = 300
y = 300x + 100
Fill in as much information as you can in the sketch tool using the following information:
JH is perpendicular to JE and HI is perpendicular to IE. Additionally, JH is congruent to HI.
Write an explanation (using proof type language) OR use the table to create a two-colum proof to as to why JE is congruent to IE
The side JE is equal to side IE because all the sides of the square are congruent.
What is a square?It is a polygon with four sides. The total interior angle is 360 degrees. In a square, all the sides of the square are equal and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
JH is opposite to JE and Hello is opposite to IE. Also, JH is congruent with HE.
Let 'm' be the side of the square.
HI = JE (Congruent)
HJ = IE (Congruent)
∠H = ∠J = ∠I = ∠E = 90°
Then the shape that is defined will be a square.
The side JE is equal to side IE because all the sides of the square are congruent.
More about the square link is given below.
https://brainly.com/question/13747846
#SPJ1
answer these questions and get 30 points
Answer: 5/4, -7/11, 1/2
Step-by-step explanation:
Slope of ordered pairs (y2-y1/x2-x1): -5/4
Y intercept (b in y=mx+b): (0, -7/11)
Slope of graph (rise over run) : 1/2
The sporting equipment has been sorted into baseballs and bats. The number of baseballs is four less than three times the number of bats. The equipment is 80% baseballs. Choose the equation that best represents this scenario.
The equation that best represents this scenario is x/(3x-4) =20/80. So, the correct option is B.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of bats be x.
The number of baseballs is four less than three times the number of bats.
The, the number of baseballs are 3x-4
The equipment is 80% baseballs. Then, the equipment is 20% bats.
So, the ratio from number of bats to number of baseballs is
x/(3x-4) =20%/80%
⇒ x/(3x-4) =20/80
Therefore, the option B is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ1
"Your question is incomplete, probably the complete question/missing part is:"
The sporting equipment has been sorted into baseballs and bats. The number of baseballs is four less than three times the number of bats. The equipment is 80% baseballs. Choose the equation that best represents this scenario
x/(3x-4) =80/20
x/(3x-4) =20/80
x/(3x-4) =80/100
x/(3x-4) =20/100
are 4:1 and 8:3 eqivalent ratios?
Answer:
No
Step-by-step explanation:
if you divide 8:3 you get 4:1.5 which is not equivalent. In order for them to be equivalent it would need to be 4:1 and 8:2
Answer: No
Step-by-step explanation:
Let's start with what we know. Ratios can also be written as fractions:
4/1 and 8/3
These fractions do not simplify to the same thing, therefore they are not equal.
write a liner function f with the given values
f(0) = -4; f(10) = -12
f(x)=
Answer:
f(x) = - x - 4----------------------
Linear function is:
f(x) = mx + b, where m- slope, b- y-interceptGiven points:
f(0) = - 4 and f(10) = - 12The first point represents the y-intercept, b = - 4.
Find the slope:
m = (-12 - (-2)) / (10 - 0) = - 10/10 = - 1The function is:
f(x) = - x - 4We want to support a thin hoop by a horizontal nail and have the hoop make one complete small-angle oscillation each 2. 0 s.
Given that the hoop makes one complete oscillation in 2s, this implies that the period of oscillation is 2s
Then,
T = 2s
Let the Mass of the thin hoop be M
Let the Radius of the hoop be R
The moment of inertial of a hoop is
I = MR²
The period of a physical pendulum of small amplitude is given by
T = 2π √(I / Mgd)
Where,
T is the period in seconds
I is the moment of inertia in kgm²
M is the mass of the hoop
g is the acceleration due to gravity
g = 9.8m/s²
d is the distance from the rotational axis to the center of gravity
Therefore, d = R
Then, applying the formula
T = 2π √ (I / MgR)
So, we know that
I = MR²
Then,
T = 2π √( MR² / MgR)
T = 2π √(R/g)
Make R the subject of the formula
Square both sides
T² = 4π²(R/g)
T²g = 4π²R
Then, R = T²g / 4 π²
Since g = 9.8m/s² and T= 2s
R = 2² × 9.8 / 4π²
R = 0.993m
Then, the radius of the hoop is 0.993m
Know more about oscillation at:
https://brainly.com/question/12622728
#SPJ4
initially alex, betty, and charlie had a total of 444444 peanuts. charlie had the most peanuts, and alex had the least. the three numbers of peanuts that each person had formed a geometric progression. alex eats 55 of his peanuts, betty eats 99 of her peanuts, and charlie eats 2525 of his peanuts. now the three numbers of peanuts each person has forms an arithmetic progression. find the number of peanuts alex had initially.
The number of peanuts that Alex had initially will compute to a total of 108 in the observations of the situation provided above.
The computation of the peanuts in the hands of Alex can easily be ascertained using the given information, and input of values from the same into the generalized formula, as shown below,
Let p be the number of peanuts. Thus, it can be stated that
3p = 444 – 9 – 25 – 5
3p = 409
p = 409/3 = 135.3
Now, it can also be stated that
p+9=144
[tex]\[\dfrac{144}{k} + 144 + k \cdot 144 = 444 \\\\ \\\dfrac{144}{k} + k \cdot 144 = 300\\\\ \\ \dfrac{12}{k} + k \cdot 12 = 25\\\\\\k= \dfrac{4}{3} \\\\\\\\ \dfrac {144\cdot 3}{4} =108}\][/tex]
Therefore, Alex has a total of 108 peanuts initially.
Learn more about computation here:
https://brainly.com/question/28171935
#SPJ4
Complete question
Initially, Alex, Betty, and Charlie had a total of 444 peanuts. Charlie had the most peanuts, and Alex had the least. The three numbers of peanuts that each person had formed a geometric progression. Alex eats 5 of his peanuts, Betty eats 9 of her peanuts, and Charlie eats 25 of his peanuts. Now, the three numbers of peanuts each person has forms an arithmetic progression. Find the number of peanuts Alex had initially.
4.) a radio station tower was built in two sections. from a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25°, and the angle of elevation of the top of the second section is 400. to the nearest foot, what is the height of the top section of the tower? (lt. 3.7
The height of the top section of the tower is 32 feet.
The radio station tower is built in two sections. The tower is 87 feet from the viewing point. The angle of elevation of the bottom section is 25 degrees. The angle of elevation from the top of tower (both sections) is 40 degrees. Let the height of the bottom section be y and height of the bottom and top section be z.
Considering a right-angled triangle, tangent formula states that:
Tan ɵ = opposite side/ adjacent side where ɵ is the angle of elevation.
Hence, when ɵ = 25, opposite side = y, and adjacent side = 87
Tan 25 = y/ 87
y = 40.57 feet
Hence, when ɵ = 40, opposite side = z, and adjacent side = 87
Tan 40 = z/87
y = 73 feet
Let the height of the top section of the tower be x.
Hence, x = 73 - 40.57 = 32.4 ≈ 32 feet
Learn more about Tangent:
https://brainly.com/question/7252502
#SPJ4
2(6-x)=3 help help help help
Answer:
x = 4.5
Step-by-step explanation:
2(6 - x) = 3 12 - 2x = 3 -2x = -9x = 4.5