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3 years ago

Help pls!! ....................................................

Mathematics

1 answer:

Nikolay [14]3 years ago

8 0

Answer:

(a) The width is 40 inches

(b) It will not

Step-by-step explanation:

Given

$D = 50$ -- Diagonal

Solving (a): H = 30 --- (height).

Find the width (W)

To do this, we make use of Pythagoras theorem

$D^2 = H^2 + W^2$

This gives:

$50^2 = 30^2 + W^2$

$2500 = 900 + W^2$

Collect Like Terms

$W^2 = 2500 - 900$

$W^2 = 1600$

Take square roots

$W = 40$

Solving (b): Will it fit into a 30 in wide cabinet?

In (a) above, we calculated the width of the TV to be 40 inches

This implies that, the width is greater than the width of the cabinet.

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78. Use properties of exponents to rewrite each expression as either an integer or as a quotient of integers p/q to show the exp

kolezko [41]

Answer:

4√2 × 4√8 = 64, an integer.

Step-by-step explanation:

a) 4√2 × 4√8

First let's remember that a square root can be rewritten as a 1/2 exponent,

Therefore the expression we have can be rewritten as

$4(2^{1/2} )4(8^{1/2})$

We are going to write all numbers in their prime factor expressions:

<u>*Note: Remember that when we multiply two numbers with the same base but different exponents we sum up the exponents*</u>

<u>*Also, when we elevate one exponent to another exponent, we multiply the exponents*</u>

$4(2^{1/2} )4(8^{1/2})\\=2^2 (2^{1/2})2^2 (2^{3})^{1/2} \\ =2^2 (2^{1/2})2^2 (2^{3/2})\\=2^22^2(2^{1/2}2^{3/2})\\=16(2^{4/2})\\=16(2^2)\\=16(4)\\=64$

Therefore, the expression 4√2 × 4√8 = 64 and therefore is an integer

4 0

3 years ago

15% of applicants for a job possess the right skills. A company has three positions to fill, and they interview applicants one a

mamaluj [8]

Answer:

a) 0.0437

b) 0.6479

c) 0.3958

Step-by-step explanation:

This is a negative binomial distribution problem. A negative binomial distribution problem describes a sequence of trials, each of which can have two outcomes (success or failure). We continue the trials indefinitely until we get r succeses.

The probability of y trials before obtaining r successes is given as

P(y) = ʸ⁻¹Cᵣ₋₁ pʳ qʸ⁻ʳ

p = 0.15

q = 1 - p = 0.85

r = 3

y = 15, ≥15 and ≤15

a) Probability of interviewing exactly 15 applicants.

p = 0.15

q = 1 - p = 0.85

r = 3

y = 15,

P(y=15) = ¹⁵⁻¹C₃₋₁ (0.15)³ (0.85)¹⁵⁻³

P(y=15) = ¹⁴C₂ (0.15)³ (0.85)¹² = 0.0436859997 = 0.0437

b) Probability of interviewing at least 15 applicants = P(y ≥ 15)

P(y ≥ 15) = 1 - P(y < 15)

P(y < 15) = P(y=3) + P(y=4) + P(y=5) + P(y=6) + P(y=7) + P(y=8) + P(y=9) + P(y=10) + P(y=11) + P(y=12) + P(y=13) + P(y=14)

= 0.003375 + 0.00860625 + 0.014630625 + 0.0207267188 + 0.0264265664 + 0.031447614 + 0.0356406292 + 0.0389501162 + 0.0413844985 + 0.0429938957 + 0.0438537736 + 0.0440531089

P(y < 15) = 0.3520887963

P(y ≥ 15) = 1 - P(y < 15) = 1 - 0.3520887963 = 0.6479112037 = 0.6479

c) Probability of interviewing at most 15 applicants

P(y ≤ 15) = P(y=3) + P(y=4) + P(y=5) + P(y=6) + P(y=7) + P(y=8) + P(y=9) + P(y=10) + P(y=11) + P(y=12) + P(y=13) + P(y=14) + P(y=15)

(y ≤ 15) = 0.003375 + 0.00860625 + 0.014630625 + 0.0207267188 + 0.0264265664 + 0.031447614 + 0.0356406292 + 0.0389501162 + 0.0413844985 + 0.0429938957 + 0.0438537736 + 0.0440531089 + 0.0436859997 = 0.395774796 = 0.3958

Hope this Helps!!!

6 0

3 years ago

Choose the equation that represents a line that passes through points -3,2 and 2,1

STatiana [176]

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{1-2}{2+3}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{1}{5}[x-(-3)]\implies y-2=-\cfrac{1}{5}(x+3)$

$\bf y-2=-\cfrac{1}{5}x-\cfrac{3}{5}\implies y=-\cfrac{1}{5}x-\cfrac{3}{5}+2\implies y=-\cfrac{1}{5}x+\cfrac{7}{5} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(y)=5\left( -\cfrac{1}{5}x+\cfrac{7}{5} \right)}\implies 5y=-x+7\implies \blacktriangleright x+5y=7 \blacktriangleleft$

4 0

3 years ago

2. In factored form, a quadratic function can be written as y= (-2- x) (x-8). This parabola goes through the points (-2, 0) and

Trava [24]

The vertex of the given parabola is the point (3, 25).

<h3>How to get the vertex of the parabola?</h3>

If the parabola has roots x₁ and x₂, then the vertex of the parabola is at:

xₙ = (x₁ + x₂)/2

Here the parabola is:

y = (-2 - x)*(x - 8)

We can rewrite that to:

y = -(x + 2)*(x - 8)

Then the two roots are:

x = -2 and x = 8

Then the vertex is at:

xₙ = (8 - 2)/2 = 6/2 = 3

To get the y-value of the vertex, we evaluate the equation in x = 3:

y = -(3+ 2)*(3 - 8) = -5*(-5) = 25

The vertex is (3, 25).

If you want to learn more about parabolas:

brainly.com/question/4061870

#SPJ1

8 0

2 years ago

30,098 in standard form <br>30,098 to four significant figures

fredd [130]

Standard form = 3.0098 × 10 power 4
Significant figures = 30100

4 0

2 years ago