Answer:
210 different mega calzones can be made.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
Additionally:
The order in which the toppings and the cheeses are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Toppings:
5 from a set of 7. So
[tex]C_{7,5} = \frac{7!}{5!2!} = 21[/tex]
Cheeses
3 from a set of 6. So
[tex]C_{6,3} = \frac{6!}{3!3!} = 20[/tex]
How many different mega calzones can be made if a mega calzone contains 5 different toppings and 3 different cheeses?
Toppings and cheeses are independent, and thus, by the fundamental counting principle:
21*20 = 210
210 different mega calzones can be made.
When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps andfound that 1304 of them were not pumping accurately (within 3.3 oz when 5 gal ispumped),and 5689 pumps were accurate. Use a 0.01 significance level to test the claimof an industryrepresentative that less than 20% of the pumps are inaccurate.
Answer:
The p-value of the test statistic from the standard normal table is 0.0017 which is less than the level of significance therefore, the null hypothesis would be rejected and it can be concluded that there is sufficient evidence to support the claim that less than 20% of the pumps are inaccurate.
Step-by-step explanation:
Here, 1304 gas pumps were not pumping accurately and 5689 pumps were accurate.
x = 1304, n = 1304 + 5689 = 6993
The level of significance = 0.01
The sample proportion of pump which is not pumping accurately can be calculated as,
The claim is that the industry representative less than 20% of the pumps are inaccurate.
The hypothesis can be constructed as:
H0: p = 0.20
H1: p < 0.20
The one-sample proportion Z test will be used.
The test statistic value can be obtained as:
[tex]Z=\frac{\hat{p}-P}{\sqrt{\frac{P(1-P))}{n}}}\\\\Z=\frac{0.186-0.20}{6993}\\\\Z=-2.927[/tex]
Sally wants to make a chocolate crunchy cake.
The recipe uses 16 biscuits and 22 squares of chocolate.
13
Sally wants to make her cake with 24 biscuits.
How many squares of chocolate will she need?
Answer:
33 squares of chocolate need
Answer:
33 Biscuits
Step-by-step explanation:
Uni method
How much biscuits do we need for 1 square of chocolate?
22/16 = 1.3
For 1 square of chocolate she needs 1.3 Biscuits.
So for 24 biscuits,
24 * 1.3
=33 biscuits
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6y - 3x = 30
Answer:
y=(x/2)+5
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept form. To get that, we need y by itself so we have to add 3x to both sides: 6y=30+3x. Now we divide by 6 and rearrange the right side: y=(3x+30)/6.
y = (3x/6)+(30/6) => y = (x/2)+5. We also know that the slope is 1/2 and the y-intercept is 5 because of the slope-intercept equation.
If p and q are the roots of 2x²+ 6x = 12 + 4x, and p < q, find q − p
Step-by-step explanation:
The given equation can be further simplified into
[tex]2x^{2}+2x-12=0[/tex]
The roots of a quadratic equation is given by
[tex]x = \dfrac{ - b \: \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
where a = 2, b = 2 and c = -12. Putting these into the roots equation, we get
[tex]x = \dfrac{ - 2 \: \pm \: \sqrt{4 \: - \: 4(2)( - 12)} }{2(2)} = \dfrac{ - 2 \: \pm \: 10}{4}[/tex]
This gives us two possible roots:
x = 2, x = -3
Since the condition is that p < q, we see that p = -3 and q = 2. Therefore,
[tex]q - p = 2 - ( - 3) = 5[/tex]
Evaluate the given equation for the indicated function values. pls help
Answer:
The answer in each numeral is:
f(4) = 28f(10) = -19f(-5) = -33f(9) = -9Step-by-step explanation:
To obtain the result in each case, you must replace the variable (n) by the value that appears in the second case, I'll explain it with the first exercise:
1. f(n) = 5n + 8 f(4) = ?As you can see, in the second doesn't appear f(n), but f(4), that means you must replace the "n" in the equation by 4, if we do this, we obtain:
1. f(4) = 5*(4) + 8f(4) = 20 + 8f(4) = 28The first answer is 28, now we'll continue with the next exercises:
2. f(n) = -2n + 1f(10) = -2*(10) + 1f(10) = -20 + 1f(10) = -193. f(n) = 6n - 3f(-5) = 6*(-5) - 3f(-5) = -30 - 3f(-5) = -334. f(n) = -nf(9) = -9In this form, you can prove the answers are: 28, -19, -33, and -9 respectively.
BC=
Round your answer to the nearest hundredth.
Answer:
1.71 = BC
Step-by-step explanation:
take 70 degree as reference angle
using cos rule
cos 70 = adjacent / hypotenuse
0.3420 = BC / 5
0.3420*5 = BC
1.71 = BC
There are approximately 1.35 billion people in China. If the world population is 7.1 billion people, what percent of the world population is in China?
Answer:
19.01%
Step-by- step explanation:
[tex]Percentage = \frac{1.35 billion }{ 7.1 billion } \times 100[/tex]
[tex]= \frac{ 1.35 \ times 1, 000, 000, 000} {7.1 \times 1,000,000,000} \times 100\\\\\\=\frac{1.35}{7.1} \times 100 = 19.01 \%[/tex]
in a club there are seven women and five men. A committee of 3 women and 2 men as to be chosen. how many different possibilities are there?
Answer:
Step-by-step explanation:
a country’s population in 1990 was 123 million in 2002 it was 128 million
Answer:
whats the question
Step-by-step explanation:
100 Brainly points!! Need help ASAP :)
In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B’. What is the scale factor of dilation?
A. 1
B. 2
C. 0.5
D. -0.5
Answer:
B
Step-by-step explanation:
I'm not really shure tho
Answer:
D. -0.5
Step-by-step explanation:
AB dilated by scale factor -0.5 to produce AB'.
the length of AB = 4 units and the length of AB' = 2 units, the direction is backward, so the scale factor is - 2/4 = -0.5
Which is the graph of the function y = 3x?
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The graph that includes the point (1, 3) will be the one that is a graph of ...
y = 3^x
09:30 to 17:00 minus 30 minutes
How many hours is that ?
Answer:
7 hours
Step-by-step explanation:
9 : 30 to 17:00 = 7 hours 30 minutes
Minus 30 minutes = 7 hours
identify the 3D shape
Answer and Step-by-step explanation:
The 3D shape shown is a rectangle. This is the net-form of a rectangle.
#teamtrees #PAW (Plant And Water)
Answer:
rectangular prism
Step-by-step explanation:
a rectangle is not 3d. a rectangle is 2d. the correct answer is a rectangular prism.
What is the value of x in this number sentence
[tex]\frac{x}{7} - 4 = 6[/tex]
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
[tex] \frac{x}{7} - 4 = 6 \\ \frac{x}{7} = 6 + 4 \\ \frac{x}{7} = 10 \\ x = 10 \times 7 \\ x = 70[/tex]
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
➳ RainbowSalt2²2² ❦
Is 4 over 5 equals 48 over 60 a true proportion?
Answer:
0.8 you yes both of them has the same answer , so it is a true portion
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
[tex]\frac{4}{5} =\frac{48}{60}[/tex]
This is a true proportion because when you cross multiply you get the same product.
[tex]48*5=240[/tex]
[tex]4*60=240[/tex]
Consider the following sets of sample data: A: $30,500, $27,500, $31,200, $24,000, $27,100, $28,600, $39,100, $36,900, $35,000, $21,400, $37,900, $27,900, $18,700, $33,100 B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answer:
[tex]CV=0.2[/tex] ---- dataset 1
[tex]CV = 7.2[/tex] --- dataset 2
Step-by-step explanation:
Given
[tex]A: 30500, 27500, 31200, 24000, 27100,28600, 39100, 36900, 35000, 21400, 37900, 27900, 18700,[/tex][tex]33100[/tex]
[tex]B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11[/tex]
Required
The coefficient of variation of each
Dataset A
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{30500+ 27500+31200+24000+ 27100+28600+ 39100+ 36900+ 35000+ 21400+ 37900+ 27900+ 18700+33100}{14}[/tex][tex]\mu = \frac{418900}{14}[/tex]
[tex]\mu = 29921.43[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(30500 - 29921.43)^2 +.................+ (18700- 29921.43)^2 + (33100- 29921.43)^2}{13}}[/tex]
[tex]\sigma= \sqrt{\frac{487723571.42857}{14}}[/tex]
[tex]\sigma= \sqrt{34837397.959184}[/tex]
[tex]\sigma= 5902.32[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV=\frac{5902.32}{29921.43}[/tex]
[tex]CV=0.2[/tex] --- approximated
Dataset B
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{4.29+ 4.88+ 4.34+ 4.17+ 4.52+ 4.80+ 3.28+ 3.79+ 4.84+ 4.77+ 3.11}{11}[/tex]
[tex]\mu = \frac{46.79}{11}[/tex]
[tex]\mu = 4.25[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{(4.29 - 4.25)^2 + (4.88- 4.25)^2 +.........+ (3.11- 4.25)^2}{11}}[/tex]
[tex]\sigma = \sqrt{\frac{3.859}{11}}[/tex]
[tex]\sigma = \sqrt{0.35081818181}[/tex]
[tex]\sigma = 0.593[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV = \frac{4.25}{0.5903}[/tex]
[tex]CV = 7.2[/tex] -- approximated
find the surface area of the composite figure
Answer:
[tex]=280[/tex] [tex]in^2[/tex]
Step-by-step explanation:
----------------------------------------
Let's find the surface area of the pink rectangular prism first.
[tex]2*10=20+20=40[/tex]
[tex]4*10=40+40=80[/tex]
[tex]4*2=8+8=16[/tex]
[tex]40+80+16=136[/tex]
The surface area for the pink rectangular prism is [tex]136[/tex] [tex]in^2[/tex].
-------------------->>>>>
Now, let's find the surface area of the green rectangular prism.
[tex]4*7=28+28=56[/tex]
[tex]4*7=28+28=56[/tex]
[tex]4*4=16+16=32[/tex]
[tex]56+56+32=144[/tex]
The surface area for the green rectangular prism is 144 [tex]in^2[/tex].
-------------------->>>>>
Now let's add the surface area of both rectangular prisms to find the surface area of the composite figure.
[tex]136+144=[/tex]
[tex]=280[/tex] [tex]in^2[/tex]
----------------------------------------
Hope this is helpful.
9514 1404 393
Answer:
224 in²
Step-by-step explanation:
There are a couple of ways to go at this. Here, we choose to figure the areas of each of the prisms individually, then subtract the "hidden" area where they are joined together.
The area of a prism is ...
A = 2(LW +H(L+W))
Pink area:
A = 2(10·4 +2(10+4)) = 2(40 +28) = 136 . . . square inches
Green area:
A = 2(7·4 +4(7+4)) = 2(28 +44) = 144 . . . square inches
One 4 in × 7 in face of the green prism meets with a similar area of the pink prism, so the area hidden at that interface is 2(4·7) = 56 square inches. Then the total surface area of the composite figure is ...
SA = 136 in² +144 in² -56 in² = 224 in²
A family uses 15 gallons of milk every 3 weeks. At that rate, about how many gallons of milk will they need to purchase in a year’s time?
Give your answer as a whole number.
They will need to purchase
Answer:
15 gallons of milk at 3 week
15/3= 5
for a month 5 * 4 =20
in a year 12 * 20 = 240
Step-by-step explanation:
4(2x + 3) ÷ 5y
The expression above provides an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write "not present."
Answer:
8xy+12y/5
Step-by-step explanation:
write the division as a fraction
4(2x+3)/5 y
Calaucte the product
4y(2x+3)/5
Distbtute 4y through the parentheis
8xy+12y/5
which gives you 8xy+12y/5
The points A(-3, -4) and B(5, 0) form a line segment. Find the coordinates of the point P that partitions segment AB in a 2:3 ratio.
Answer:
Step-by-step explanation:
let the coordinates of P be (x,y)
[tex]x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n} \\x=\frac{2(5)+3(-3)}{2+3} \\x=\frac{10-9}{5} =\frac{1}{5} =0.2\\y=\frac{2(0)+3(-4)}{2+3} \\y=\frac{0-12}{5} =\frac{-12}{5} =-2.4\\[/tex]
so coordinates of P are (0.2,-2.4)
please answer i will mark brainliest :)
Answer:
c I think that's the right answer
someone pls help ill give you a kiss and a cookie fi you help meee
for the point (6,8) find the csc theta and sec theta
Answer:
cscθ = 5/4, secθ = 5/3
Step-by-step explanation:
First, let's view the drawing that I have attached, with the dot in the bottom left representing the origin. We know that cosecant and secant are the reciprocals of sin and cos respectively, and in order to find sin and cos, we must find the opposite, adjacent, and hypotenuse sides. The hypotenuse is opposite the right angle, equal to √(8²+6²) = 10
Next, we can find sin and cos of θ . sinθ = 8/10=4/5, making cscθ the reciprocal of 4/5, or 5/4
Similarly, cosθ = 6/10=3/5, and secθ = 5/3
find the area of the given figure
[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
Radius of the circle "[tex]r[/tex]" = 5.5 yd
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The area of the given figure.
[tex]\sf \bf {\boxed {\mathbb {SOLUTION :}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {b. \:47.5\:sq\:yd.}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
We know that,
[tex]\sf\pink{Area\:of\:a\:semi-circle}[/tex] = [tex]\frac{\pi \: {r}^{2} }{2} [/tex]
Using 3.14 for π, we have
[tex] = \frac{3.14 \times ( {5.5 \: yd})^{2} }{2} \\[/tex]
[tex] = \frac{3.14 \times 5.5 \times 5.5 \: {yd}^{2} }{2}\\ [/tex]
[tex] = \frac{94.985 \: {yd}^{2} }{2} \\[/tex]
[tex] = 47.5 \: {yd}^{2} \\[/tex]
Using [tex]\frac{22}{7} [/tex] for π,
[tex] = \frac{22 \times 5.5 \times 5.5 \: {yd}^{2} }{7 \times 2} \\[/tex]
[tex] = \frac{665.5 \: {yd}^{2} }{14}\\ [/tex]
[tex] = 47.5 \: {yd}^{2} \\[/tex]
Therefore, the area of the semi-circle is [tex]47.5\: yd²[/tex].
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
Given the triangle below, what is the length of the third side, rounded to the
nearest whole number?
B
18
A
12
620
Triangle not drawn to scale
A. 18
B. 14
C. 16
D. 20
Answer:
Option C
Step-by-step explanation:
In this question measure of two sides and and the angle between these sides of a triangle is given.
We have to calculate the measure of third side.
By applying cosine rule in the given triangle.
BC² = AB² + AC² - 2(AB)(AC)cos(A)
BC² = (18)² + (12)² - 2(18)(12)cos(62°)
BC² = 324 + 144 - 202.81
BC² = 265.19
BC = 16.28
BC ≈ 16 units
Therefore, Option C will be the correct option.
can someone help me with this?
Answer: 22
Step-by-step explanation: 44:2=22
PLEASE HELP ME WITH THIS ONE QUESTION
How many combinations with repetition are allowed if n = 6 and r = 3?
A) 27
B) 20
C) 18
D) 56
Answer:
D. 56
Step-by-step explanation:
The general solution for the number of combinations with repetition is represented by the following expression:
[tex]x = \frac{(n + r - 1)!}{r!\cdot (n-1)!}[/tex] (1)
Where:
[tex]n[/tex] - Total number of elements.
[tex]r[/tex] - Number of the sample.
If we know that [tex]n = 6[/tex] and [tex]r = 3[/tex], then the number of combinations with repetition:
[tex]x = \frac{(6+3-1)!}{3!\cdot (6-1)!}[/tex]
[tex]x = 56[/tex]
Hence, correct answer is D.
Helppppppp
Which choice is equivalent to the product below
Step-by-step explanation:
jkkkkkkkkkkkkkkkkkkkkk
Answer:
[tex]2 \sqrt{35} [/tex]
Having trouble with these questions, please help.
Answer:
(a)=50%(b)=2.1and(c)=16.1
Step-by-step explanation:
Hope this helps
please solve in the next 10 minutes pleaseeee
Answer:
43.82 mph
266.67 feet
Step-by-step explanation:
Given :
S = √30fl
S = speed of car
f = drag Coefficient
l = Length of skid mark
If f = 0.8 ; l = 80 feets
s = √30fl
s = √(30*0.8*80)
s = √1920
s = 43.817
s = 43.82 mph
B.)
s = 80 mph
f = 0.8
s = √30fl
80 = √30*0.8*l
80 = √24l
Square both sides
80² = 24l
6400 = 24l
l = 6400/24
l = 266.67 feets
7/7q+21= x /5q^2-45 then x=?
Answer:
x = 5q - 15
Step-by-step explanation:
[tex]\frac{7}{7q+21}=\frac{x}{5q^{2}-45}\\\\\frac{7}{7(q+3)}=\frac{x}{5 (q^{2} -9)}\\\\frac{1}{q+3}=\frac{x}{5*(q^{2}-3^{2})}\\\\\frac{1}{q+3}=\frac{x}{5(q+3)(q-3)}\\\\\frac{1}{q+3}*5*(q+3)(q-3)=x\\\\5(q-3)=x\\\\x= 5q-15[/tex]
