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2 years ago

5

Math your class is holding elections to choose a leadership committee of 4 students. if there are 30 students in the class, how

many different leadership committees would it be possible to elect?

1 answer:

inessss [21]2 years ago

7 0

That would be 30C4 - combinations of 4 from 30.

= 30*29*28*27
---------------- = 27,405 Answer
4 * 3 * 2 * 1

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Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a

viktelen [127]

Answer:

A. One pound of pistachios plus 1 pound of almonds cost $20

C. Reducing the number of pounds of almonds by 1 results in a total cost of $40.

E. The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let

x ----> the cost of one pound pistachios

y ----> the cost of one pound of almonds

we know that

x=y+4 -----> equation A

2x+3y=48 -----> equation B

substitute equation A in equation B and solve for y

2(y+4)+3y=48

2y+8+3y=48

5y=48-8

y=8

Find the value of x

x=8+4 =12

therefore

The cost of one pound pistachios is $12 and the cost of one pound of almonds is $8

<em>Verify all statements</em>

case A) One pound of pistachios plus 1 pound of almonds cost $20.

Is True

x+y=$12+$8=$20

case B) The pistachios cost twice as much per pound as the almonds

Is false

Because

2y=2(8)=$16

$16≠$12

case C) Reducing the number of pounds of almonds by 1 results in a total cost of $40

Is True

Because

2x+2y=2(12)+2(8)=$40

case D) The cost a, in dollars, of 1 pound of almonds is modeled by 2(a – 4) + 3a = 48.

Is false

The equation will be

2(a + 4) + 3a = 48.

case E) The cost p, in dollars, of 1 pound of pistachios is modeled by 2p + 3(p – 4) = 48

Is true

Because

p=a+4

Solve for a

a=p-4

8 0

2 years ago

A rectangular lot is bounded on one side by a river and on the other three sides by a total of 80m of fencing. Find the dimensio

vova2212 [387]

Hello,

Let 's a the width,
b the heigth

2a+b=80==>b=80-2a

Area=A(a,b)=a*b=a*(80-2a)
=-2a²+80a
=-2(a²-2*20a+20²-20²)
=-2(a-20)² +800
Area is maxi if a=20 and area max=800

5 0

2 years ago

PROBLEM SOLVING Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during

Akimi4 [234]

Answer:

Probability that at most 50 seals were observed during a randomly chosen survey is 0.0516.

Step-by-step explanation:

We are given that Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each survey.

The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals.

Let X = <u><em>numbers of seals observed</em></u>

The z score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean numbers of seals = 73

$\sigma$ = standard deviation = 14.1

Now, the probability that at most 50 seals were observed during a randomly chosen survey is given by = P(X $\leq$ 50 seals)

P(X $\leq$ 50) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{50-73}{14.1}$ ) = P(Z $\leq$ -1.63) = 1 - P(Z < 1.63)

= 1 - 0.94845 = <u>0.0516</u>

The above probability is calculated by looking at the value of x = 1.63 in the z table which has an area of 0.94845.

4 0

2 years ago

Which of the following are true statements about David Hilbert?

Lunna [17]

Answer:

he invented the point

he was a German mathematician

he Hilbert's improvements to geometry are still used in textbooks today

he developed Hilbert's axioms

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Evaluate the double integral. 9y2 da, d is the triangular region with vertices (0, 1), (1, 2), (4, 1) d

Rudik [331]

Consider this option (see the attachment).
If it is possible, check it in other sources.

6 0

2 years ago