Answer:
226 teams
Step-by-step explanation:
A team can be:
5 girls4 girls and 1 boy3 girls and 2 boys2 girls and 3 boysCount all combinations:
1. 5 girls from 5 girls can be chosen in 1 way.
2. 4 girls from 5 girls can be chosen in
[tex]C^5_4=\dfrac{5!}{4!(5-4)!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 4\cdot 1}=5[/tex]
different ways and 1 boy from 5 boys can be chosen in
[tex]C^5_1=\dfrac{5!}{1!(5-1)!}=\dfrac{5!}{1!\cdot 4!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 4\cdot 1}=5[/tex]
different ways, so in total,
[tex]5\cdot 5=25[/tex]
different combinations.
3. 3 girls from 5 girls can be chosen in
[tex]C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2}=10[/tex]
different ways and 2 boys from 5 boys can be chosen in
[tex]C^5_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5!}{2!\cdot 3!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 1\cdot 2\cdot 3}=10[/tex]
different ways, so in total,
[tex]10\cdot 10=100[/tex]
different combinations.
4. 2 girls from 5 girls can be chosen in
[tex]C^5_2=\dfrac{5!}{2!(5-2)!}=\dfrac{5!}{2!\cdot 3!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 1\cdot 2\cdot 3}=10[/tex]
different ways and 3 boys from 5 boys can be chosen in
[tex]C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2}=10[/tex]
different ways, so in total,
[tex]10\cdot 10=100[/tex]
different combinations.
In total, there are
[tex]1+25+100+100=226[/tex]
possible teams.
One polygon has a side of length 3 feet. A similar polygon has a corresponding side of length 9 feet. The ratio of the perimeter of the smaller polygon to the larger is 3:1 1:6 1:3
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill \\\\ \cfrac{\textit{small polygon}}{\textit{large polygon}}\qquad \qquad \cfrac{3}{9}\implies \cfrac{1}{3}\implies \stackrel{ratio}{1:3}[/tex]
Which division problems have quotients of 682? Check all that apply.
(600 + 80 + 2) = 10
(6,000 + 800 F 20) = 10
(60,000 + 8,000 + 200) = 100
682,000 = 1,000
6,820,000 = 1,000
Answer:
(6,000 + 800 +20) /10
(60,000 + 8,000 + 200) / 100
682,000 / 1,000
Step-by-step explanation:
Use a calculator
Do the parenthesis first and divide
The division problems that result in a quotient of 682 are 682,000 ÷ 1,000 and 6,820,000 ÷ 10,000. This is because when we divide these large sums by their respective divisors, we get 682 as the quotient.
Explanation:To figure out which division problems result in a quotient of 682, we need to remember how division works. Division is basically the opposite of multiplication - if you multiply the quotient by the divisor, you should get the dividend. Essentially, we're looking for problems where we divide a total (dividend) by a number (divisor) and get 682 (quotient).
For instance, if we were to have a division problem like 682,000 ÷ 1,000, we would get 682 as our quotient. The same would be true for 6,820,000 ÷ 10,000, where the quotient would also be 682.
However, the problems such as (600 + 80 + 2) ÷ 10, and (60,000 + 8,000 + 200) ÷ 100 do not result in a quotient of 682 and therefore don't apply. So only the two problems with the larger sums (682,000 ÷ 1,000 and 6,820,000 ÷ 10,000) are valid solutions.
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please help meeeeeeeeee
Answer:
c
Step-by-step explanation:
ANSWER
A. 12
EXPLANATION
From the stem-and-leaf plot, the trees that are between 610 inches tall and 640 inches tall are:
613,616,622,622,624,625,631,631,633,637,637,and 638.
Counting the number of trees gives 12 of them.
Therefore, the number of trees that are between 610 inches tall and 640 inches tall is 12.
The correct answer is A.
The scores on a quiz are normally distributed. The mean of the quiz is 93 and the standard deviation is 4.2. By using the Empirical rule, what scores fall 1 standard deviation from the mean?
89 and 101
84.6 and 101.4
89.2 and 96.8
88.8 and 97.2
Answer:
any score that lies between 88.8 and 97.2 is within one std. dev. of the mean
Step-by-step explanation:
One std. dev. above the mean would be 93 + 4.2, or 97.2. One std. dev. below the mean would be 93 - 4.2, or 88.8.
So: any score that lies between 88.8 and 97.2 is within one std. dev. of the mean.
The scores that fall within one standard deviation of the mean are between 88.8 and 97.2. This matches the last option provided.
The Empirical Rule helps us understand how data is distributed in a normal distribution. The rule states that approximately 68% of the data falls within one standard deviation of the mean.
Given a mean (μ) of 93 and a standard deviation (σ) of 4.2, we calculate the range within one standard deviation:
Subtract one standard deviation from the mean: 93 - 4.2 = 88.8Add one standard deviation to the mean: 93 + 4.2 = 97.2Therefore, the scores that fall within one standard deviation of the mean are between 88.8 and 97.2, which matches the last option.
The point ( -2,-1) satisfies which of the following inequalities?
Answer:
-5x+2y+1>0
Step-by-step explanation:
Plug in -2 for x and -1 for y. This is the only answer that gives you a positive number that is greater than zero.
Answer: Second Option
Step-by-step explanation:
Substitute the point in each of the given inequalities and verify if the inequality is met.
If the inequality is fulfilled then the point belongs to the region
For
[tex]5x-2y +1>0[/tex]
[tex]5(-2)-2(-1) +1>0[/tex]
[tex]-10+2 +1>0[/tex]
[tex]-7>0[/tex]
-7 is not greater than zero. the inequality is not met
For
[tex]-5x+2y +1>0[/tex]
[tex]-5(-2)+2(-1) +1>0[/tex]
[tex]10-2 +1>0[/tex]
[tex]9>0[/tex]
9 is greater than zero. So the point belongs to inequality
For
[tex]-2x+5y -1>0[/tex]
[tex]-2(-2)+5(-1) -1>0[/tex]
[tex]4-5-1>0[/tex]
[tex]-2>0[/tex]
-2 is not greater than zero. the inequality is not met
For
[tex]2x+5y -1>0[/tex]
[tex]2(-2)+5(-1) -1>0[/tex]
[tex]-4-5 -1>0[/tex]
[tex]-10>0[/tex]
-10 is not greater than zero. the inequality is not met
Factor the following 3z^2+26z-9
Answer:
(3z - 1)(z + 9)
Step-by-step explanation:
Answer:
(z + 9)(3z - 1)
Step-by-step explanation:
Given
3z² + 26z - 9
To factor the quadratic
Consider the factors of the product of the z² term and the constant term which sum to give the coefficient of the z- term
product = 3 × - 9 = - 27 and sum = + 26
The factors are + 27 and - 1
Use these factors to split the z- term
3z² + 27z - z - 9 ( factor the first/second and third/fourth terms )
3z(z + 9) - 1(z + 9) ← factor out (z + 9) from each term
(z + 9)(3z - 1) ← in factored form
At a summer camp, there are 50 girls out of 80 campers.What is this ratio writtin as a fraction in simplest form?
The ratio is 5:8 campers
Answer:
50
--- Ratio: 50:80
80
Step-by-step explanation:
50 would be how many girls were that the summer camp. And the 80 is how many students all together at the summer camp.
Hoped This Helped You
Have A Wonderful day
For a polygon with n sides, 180(n - 2) will give the sum of the ____ angles.
Answer:
Interior
Step-by-step explanation:
The sum of the interior angles of a polygol with n sides is 180(n-2)
Answer:
Interior
Step-by-step explanation:
What is the surface area of this composite solid?
square feet
let's take a peek
we really have a rectangular prism below a square pyramid.
the prism has a front, back, left and right of a rectangle 2x11 .
its bottom or base is an 11x11 square.
the pyramid 4 triangles, each one has a base of 11 and a height of 7.
[tex]\bf \stackrel{\textit{front, back, left, right}}{4(2\cdot 11)}~~+~~\stackrel{\textit{base}}{(11\cdot 11)}~~+~~\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(11)(7) \right]} \\\\\\ 88+121+154\implies 363[/tex]
Answer:
The surface area of composite solid = 363 ft²
Step-by-step explanation:
Points to remember
Area of rectangle = Length * Breadth
Area of triangle = bh/2
Where b - Base and h - Height
To find the surface area of composite solid
Surface area = Base area + side area + area of 4 triangles
= (11 * 11) + 4(11 * 2) + 4(11 * 7)/2
= 121 + 88 + 154
= 363 ft²
Therefore the surface area of composite solid = 363 ft²
What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5 x + 10 and passes through the point (15, –5)?
The equation of the line in slope-intercept form is y = -5/3 x +
Answer:
[tex]\large\boxed{y-intercept=20}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{3}{5}x+10\to m_1=\dfrac{3}{5}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{3}{5}}=-\dfrac{5}{3}.\\\\\text{The equation of the searched line:}\ y=-\dfrac{5}{3}x+b.\\\\\text{The line passes through }(15,\ -5).[/tex]
[tex]\text{Put thecoordinates of the point to the equation.}\ x=15,\ y=-5:\\\\-5=-\dfrac{5}{3}(15)+b\\\\-5=(-5)(5)+b\\\\-5=-25+b\qquad\text{add 25 to both sides}\\\\b=20\\\\\boxed{y=-\dfrac{5}{3}x+20}[/tex]
which expression is equivalent to (64y^100)^1/2
Answer:
8y^50
Step-by-step explanation:
Answer:
8y^50
Step-by-step explanation:
Can someone help me out with this question plz
Answer:
[tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]
[tex]\left(s-t\right)\left(x\right)=-x[/tex]
[tex]\left(s+t\right)\left(4\right)=20[/tex]
Step-by-step explanation:
Given functions are:
[tex]s\left(x\right)=x+4[/tex]
[tex]t\left(x\right)=2x+4[/tex]
Then [tex]\left(s\cdot t\right)\left(x\right)=s\left(x\right)\cdot t\left(x\right)[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=\left(x+4\right)\left(2x+4\right)[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+4x+8x+16[/tex]
or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]
---------
Similarly
[tex]\left(s-t\right)\left(x\right)=s\left(x\right)-t\left(x\right)[/tex]
or [tex]\left(s-t\right)\left(x\right)=\left(x+4\right)-\left(2x+4\right)=x+4-2x-4[/tex]
or [tex]\left(s-t\right)\left(x\right)=-x[/tex]
---------
Similarly
[tex]\left(s+t\right)\left(4\right)=s\left(4\right)+t\left(4\right)=\left(4+4\right)+\left(2\left(4\right)+4\right)=\left(8\right)+\left(12\right)=20[/tex]
[tex]\left(s+t\right)\left(4\right)=20[/tex]
find the value of 3x/2 - 7 if x =8
Answer:
( ( 3(8) ) /2 ) - 7 = 5
Step-by-step explanation:
Eliminate the denominator by reducing the fraction by 2
3(4) - 7
Solve:
12 - 7
= 5
Answer:
5
Step-by-step explanation:
Given
[tex]\frac{3x}{2}[/tex] - 7
To evaluate substitute x = 8 into the expression
[tex]\frac{3(8)}{2}[/tex] - 7 = [tex]\frac{24}{2}[/tex] - 7 = 12 - 7 = 5
9 is subtracted from 5 times 3 and 10 is added
The final answer is 16
What is subtraction?The act or process of taking one number away from another is called subtraction.
How to now the final value after subtraction?According to the problem,
9 is subtracted from 5 times 3 and 10 is addedThis can be written as (5 x 3) + 10- 9
= 16
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Describe each locus of points
30. The set of all points in space that are a distance 6 in. from line AB
Answer:
. from line l. In a coordinate plane, the locus of points 5 units ... 30. * .. ... The distance between parallel lines 6 and m is 12 units. Point A is on ...
Step-by-step explanation:
The distance between two cities is 500 miles. On a map, they are 4 inches apart. What is the scale of the map?
500/4 = x/1
125 = x
125 miles per inch.
At which point(s) do the graphs of y = x + 1 and y = 2x intersect?
Answer:
(1,2)
Step-by-step explanation:
I just used a graphing calculator
HELP ME PLEASE!!!!I BEGG YOUUUU PLEASE IM STUCK!!!
Hello There!
All of the areas are indeed perfect squares.
4x4 is 16
5x5 is 25
3x3 is 9
A right rectangular prism with square bases has a height of 20 centimeters and a volume of 800 cubic centimeters.
Which statements describe the prism? Check all that apply.
The prism is a cube.
The diagonal of the base is 4 centimeters.
The length of a side of the base is 20 centimeters.
The area of a base is 40 square centimeters.
The area of a lateral side between the bases is about 126.5 square centimeters.
Answer:
The length of a side of the base is 20 centimeters.
The area of a lateral side between the bases is about 126.5 square centimeters.
Step-by-step explanation:
It's a rectangular prism with a total volume of 800 cu cm, and a height of 20 cm.
So, the base has an area of... 800/20 = 40 sq cm.
The prism is a cube. NO. If it was a cube, the base would be 400 sq cm (20x20), since the height is 20.
The diagonal of the base is 4 centimeters. NO. with a base of 40 sq cm, it's impossible to have a diagonal of 4 cm. A diagonal would form a hypotenuse... and an hypotenuse is longer than the two other sides... an hypotenuse of 4 would mean for example sides of about 2 and 3... which gives 6 sq cm for the base, not 40.
The length of a side of the base is 20 centimeters. COULD BE. The base is 40 sq cm, it could have a side of 20 and the other of 2. Without knowing more about the prism than what's included in the question, we can't say YES and we can't say NO.
The area of a base is 40 square centimeters. Yes
The area of a lateral side between the bases is about 126.5 square centimeters. YES, since the height is 20, that would mean one side of the base would be roughly 6.325 cm... for a base area of 6.325 x 6.325 = 40 sq cm.
1. The area of a base is 40 square centimeters.
2. The area of a lateral side between the bases is about 126.5 square centimeters.
Step-by-step explanation:The statements that describe the prism are:
1. The area of a base is 40 square centimeters.
To find the volume of any rectangular prism, we use the formula [tex]base \times height[/tex].
It is given that the volume of prism is 800 cubic centimeters and height is 20 centimeters.
Putting these values in the volume formula, to find base(B):
[tex]800=B(20)[/tex]
[tex]B=40[/tex]
Hence, area of base is 40 square centimeters.
2. The area of a lateral side between the bases is about 126.5 square centimeters.
A number increase by 7 is greater than 30
Answer:
x > 23
Step-by-step explanation:
Subtract 7 on both sides in the equation: x + 7 > 30
You will get x > 23
Samara is adjusting a satellite because she finds it is not focusing the income radio waves perfectly. The shape of her satellite can be modeled by (y-3)^2 = 8(x-4) where x and y are modeled in inches. She realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite? (-3,-6) (-3,-4) (3,6) 6,3)
Answer:
[tex]\boxed{\text{(6, 3)}}[/tex]
Step-by-step explanation:
The conic form of the equation for a sideways parabola is
(y - k)² = 4p(x - h)
The focus is at (h + p, k)
The equation of Samara's parabola is
(y - 3)² = 8(x - 4)
h = 4
p = 8/4 = 2
k = 3
h + p = 6
So, the focus point of the satellite dish is at
[tex]\boxed{\textbf{(6, 3)}}[/tex]
Jeff made $243.75 last week. If he worked 25 hours, how much is he paid for one hour of work?
Answer:
$9.75
Step-by-step explanation:
Answer:
Step-by-step explanation: $9.75 per hour
243.75/25= 9.75
PLEASE HELP ASAP!!! Fill in a two-column proof for the following conjecture. Use the reasons in the bank below, you will not use them all and can use any more than once if needed
Answer:
2. Given
3. Definition of supplementary angles
4. Substitution Property
5 Subtraction Property
Step-by-step explanation:
2. Given
We are given in the statement that m<1 = 112°
3. Definition of supplementary angles
Supplementary angles definition: Two angles are supplementary if there sum is equal to 180°. That statement states:
m<1 + m<2 = 180°
4. Substitution Property
We put the value of m<1 = 112° in the equation. This is substitution property.
5. Subtraction Property
To find the value of m<2 we subtract 112 from both sides of the equation.
This is subtraction property.
11-30x+24. what is this answer
Answer:
-30x+35
Step-by-step explanation:
Add 11 and 24
Please help asap!! Read carefully
Answer:
one x-intercept.
Transformation: shift to the right 8 units.
Step-by-step explanation:
The parent function is [tex]f(t)=t^{2}[/tex]
To find the number of x-intercepts, we equate the function to zero.
[tex]\implies t^{2}=0[/tex]
[tex]\implies t=0[/tex]
There is only one x-intercept at t=0.
The transformed function is
[tex]g(t)=(t-8)^2[/tex]
This function is obtained shifting the parent function 8 units to the right.
The x-intercept will now be at t=8.
Hence the image function also has one x-intercept.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
[tex]-\sqrt{11}[/tex]
Step-by-step explanation:
As square root value is written with both + and - signs
In Given case:
A polynomial has root [tex]\sqrt{11}[/tex]
= ±3.316
Also [tex]-\sqrt{11}[/tex]
= ±3.316
Hence [tex]-\sqrt{11}[/tex] is also root of the polynomial!
how do you make a vegetable necklace? middle school math with pizzazz! book E
The question from 'Middle School Math with Pizzazz! Book E' appears to utilize pie as a topic to explore fractions. It illustrates fractions visually, such as expressing three out of five slices of pie as 3/5, or six out of ten slices as 6/10 (which simplifies to 3/5).
Explanation:The question seems to be from the 'Middle School Math with Pizzazz! Book E'. It doesn’t seem to relate directly to the creation of a vegetable necklace, but I can infer that it relates to the concept of fractions, as suggested in the information. In mathematical terms, the slicing of pies and selection of pieces can be equated to the division of a whole into smaller parts, which is how fractions are defined.
For example, slicing one pie into five slices and taking three of them can be represented as 3/5, or three-fifths. This represents the concept of fractions in an easy-to-understand, visual way. Similarly, splitting one pie into 10 pieces and selecting 6 can be expressed as 6/10, or six-tenths, which also reduces to three-fifths when simplified.
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Final answer:
The 'vegetable necklace' problem seems to be a math-related craft activity aimed at teaching fractions or ratios. It involves creating a necklace pattern with vegetables in a consistent ratio, providing a hands-on way to understand these mathematical concepts in middle school math.
Explanation:
The question appears to be from a workbook called Middle School Math With Pizzazz! Book E, which suggests that the problem is related to a math puzzle or activity. Although the question mentions making a vegetable necklace, this is likely a math-based craft or theoretically presented problem for representing fractions, ratios, or patterns that are common in middle school mathematics.
Based on the provided reference (A.1), we can understand that this problem might be connected to fractions or proportional reasoning. The example given explains how we can divide pies into slices to represent different fractions yet end up with the same quantity. This principle can be applied to making a necklace, where vegetables represent parts of a whole, and different combinations can result in a necklace of the same length or number of items.
To make a vegetable necklace, a student could take a string and add vegetables at regular intervals, ensuring that the pattern or ratio remains consistent. For instance, if the pattern is one carrot for every two tomatoes, and the length of the necklace is to have 15 vegetables, there would be 5 carrots and 10 tomatoes on the string, maintaining the ratio.
This activity would give them a tangible representation of fractions and ratios, providing a hands-on experience in understanding these mathematical concepts.
The histogram shows the weekly attendance of participants in a school's study skills program. Student attendance numbers were the same during which two weeks of the workshop?
A.
weeks 1 and 2
B.
weeks 2 and 4
C.
weeks 5 and 6
D.
weeks 4 and 6
That would be week 2 and 4 (B). They are both at 12 students attending
Hope this helped!
Answer:
The correct option is B. weeks 2 and 4.
Step-by-step explanation:
Consider the provided histogram.
The histogram shows the weekly attendance of participants in a school's study skills program.
Now, consider the Histogram.
In week 1 the Student attendance was 8.
In week 2 the Student attendance was 12.
In week 3 the Student attendance was 15.
In week 4 the Student attendance was 12.
In week 5 the Student attendance was 18.
In week 6 the Student attendance was 16.
Hence the Student attendance numbers were the same during week 2 and week 4 of the workshop.
Therefore, the correct option is B. weeks 2 and 4
Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
Square root of the quantity x-6 end quantity - 4 =x
Answer:
x=-2 is the only solution
Step-by-step explanation:
The given equation is
[tex]\sqrt{x+6}-4=x[/tex]
Add 4 to both sides of the equation.
[tex]\sqrt{x+6}=x+4[/tex]
Square both sides
[tex]x+6=(x+4)^2[/tex]
[tex]x+6=x^2+8x+16[/tex]
Rewrite in standard form;
[tex]x^2+8x-x+16-6=0[/tex]
[tex]x^2+7x+10=0[/tex]
[tex]x^2+7x+10=0[/tex]
[tex](x+2)(x+5)=0[/tex]
x=-2 or x=-5
Checking for extraneous solution.
When x=-2
[tex]\sqrt{-2+6}-4=-2[/tex]
[tex]\sqrt{4}-4=-2[/tex]
[tex]2-4=-2[/tex]. This statement is true. This implies that: x=-2 is a solution.
When x=-5
[tex]\sqrt{-5+6}-4=-5[/tex]
[tex]\sqrt{1}-4=-5[/tex]
[tex]1-4=-5[/tex]. This statement is not true. This implies that: x=-5 is an extranous solution.
Hello! :)
Please help me. Thanks!
~ Destiny ^_^
Answer:
720 in³
Step-by-step explanation:
The volume (V) of a right prism is calculated as
V = area of triangular end × length
area of Δ = [tex]\frac{1}{2}[/tex] bh
where b is the base and h the perpendicular height
here b = 8 and h = 15, thus
area of Δ = 0.5 × 8 × 15 = 4 × 15 = 60 in²
The length of the prism is 12 in, hence
V = 60 × 12 = 720 in³