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3 years ago

I WILL GIVE BRAINLIEST!! NO LINKS PLZ 4) Simplify.

Mathematics

2 answers:

zloy xaker [14]3 years ago

7 0

Answer: $\frac{\sqrt{5}}{6}$

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Work Shown:

$\frac{\sqrt{10}}{3\sqrt{8}}\\\\\frac{\sqrt{10}*\sqrt{8}}{3\sqrt{8}*\sqrt{8}}\\\\\frac{\sqrt{10*8}}{3\sqrt{8*8}}\\\\\frac{\sqrt{80}}{3\sqrt{64}}\\\\\frac{\sqrt{80}}{3*8}\\\\\frac{\sqrt{16*5}}{24}\\\\\frac{\sqrt{16}*\sqrt{5}}{24}\\\\\frac{4*\sqrt{5}}{24}\\\\\frac{\sqrt{5}}{6}\\\\$

Note: In the second step, I multiplied top and bottom by $\sqrt{8}$ to rationalize the denominator.

bezimeni [28]3 years ago

7 0

Answer:

square root of 5 over 6 or 0.37267799…

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate.

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What’s the measure of the angle theta?

11111nata11111 [884]

Answer:

∅ = 50°

Step-by-step explanation:

YOU NEED A CALCULATOR TO SOLVE THIS!

You need to use Law of Sines

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Here you will be doing $\frac{a}{sinA} =\frac{c}{sinC}$

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3 years ago

Marsia will make a frame for her picture the length of the picture is 15 inches the width is 1/3 of the length how much wood doe

marysya [2.9K]

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3 years ago

Three consecutive natural numbers have a sum of 36. What is the greatest number?

Eduardwww [97]

It's 12 because if you divide 36 by 3 (consecutive) it equals 12

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3 years ago

Read 2 more answers

NO LINKS!!! What is the equation of these two graphs?

S_A_V [24]

Answer:

$\textsf{1.} \quad y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}\:\:\textsf{ where}\:\:x \geq \dfrac{15-\sqrt{769}}{2}\\\\\quad \textsf{or} \quad y=2\sqrt{x+5}$

$\textsf{2.} \quad y=-|x+1|+5$

Step-by-step explanation:

<h3>Question 1</h3>

Method 1 - modelling as a quadratic with restricted domain

Assuming that the points given on the graph are points that the curve passes through, the curve can be modeled as a quadratic with a limited domain. Please note that as the x-intercept has not been defined on the graph, I am not including this in this first method.

Standard form of a quadratic equation:

$y=ax^2+bx+c$

Given points:

(-4, 2)
(-1, 4)
(4, 6)

Substitute the given points into the equation to create 3 equations:

Equation 1 (-4, 2)

$\implies a(-4)^2+b(-4)+c=2$

$\implies 16a-4b+c=2$

Equation 2 (-1, 4)

$\implies a(-1)^2+b(-1)+c=4$

$\implies a-b+c=4$

Equation 3 (4, 6)

$\implies a(4)^2+b(4)+c=6$

$\implies 16a+4b+c=6$

Subtract Equation 1 from Equation 3 to eliminate variables a and c:

$\implies (16a+4b+c)-(16a-4b+c)=6-2$

$\implies 8b=4$

$\implies b=\dfrac{4}{8}$

$\implies b=\dfrac{1}{2}$

Subtract Equation 2 from Equation 3 to eliminate variable c:

$\implies (16a+4b+c)-(a-b+c)=6-4$

$\implies 15a+5b=2$

$\implies 15a=2-5b$

$\implies a=\dfrac{2-5b}{15}$

Substitute found value of b into the expression for a and solve for a:

$\implies a=\dfrac{2-5(\frac{1}{2})}{15}$

$\implies a=-\dfrac{1}{30}$

Substitute found values of a and b into Equation 2 and solve for c:

$\implies a-b+c=4$

$\implies -\dfrac{1}{30}-\dfrac{1}{2}+c=4$

$\implies c=\dfrac{68}{15}$

Therefore, the equation of the graph is:

$y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}$

$\textsf{with the restricted domain}: \quad x \geq \dfrac{15-\sqrt{769}}{2}$

Method 2 - modelling as a square root function

Assuming that the points given on the graph are points that the curve passes through, and the x-intercept should be included, we can model this curve as a square root function.

Given points:

(-4, 2)
(-1, 4)
(4, 6)
(0, -5)

The parent function is:

$y=\sqrt{x}$

Translated 5 units left so that the x-intercept is (0, -5):

$\implies y=\sqrt{x+5}$

The curve is stretched vertically, so:

$\implies y=a\sqrt{x+5} \quad \textsf{(where a is some constant)}$

To find a, substitute the coordinates of the given points:

$\implies a\sqrt{-4+5}=2$

$\implies a=2$

$\implies a\sqrt{-1+5}=4$

$\implies 2a=4$

$\implies a=2$

$\implies a\sqrt{4+5}=6$

$\implies 3a=6$

$\implies a=2$

As the value of a is the same for all points, the equation of the line is:

$y=2\sqrt{x+5}$

<h3>Question 2</h3>

Vertex form of an absolute value function

$f(x)=a|x-h|+k$

where:

(h, k) is the vertex
a is some constant

From inspection of the given graph:

vertex = (-1, 5)
point on graph = (0, 4)

Substitute the given values into the function and solve for a:

$\implies a|0-(-1)|+5=4$

$\implies a+5=4$

$\implies a=-1$

Substituting the given vertex and the found value of a into the function, the equation of the graph is:

$y=-|x+1|+5$

7 0

1 year ago

Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat. Because most of the body’s

irakobra [83]

Answer:

No, because the 95% confidence interval contains the hypothesized value of zero.

Step-by-step explanation:

Hello!

You have the information regarding two calcium supplements.

X₁: Calcium content of supplement 1

n₁= 12

X[bar]₁= 1000mg

S₁= 23 mg

X₂: Calcium content of supplement 2

n₂= 15

X[bar]₂= 1016mg

S₂= 24mg

It is known that X₁~N(μ₁; σ²₁), X₂~N(μ₂;δ²₂) and σ²₁=δ²₂=?

The claim is that both supplements have the same average calcium content:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

α: 0.05

The confidence level and significance level are to be complementary, so if 1 - α: 0.95 then α:0.05

since these are two independent samples from normal populations and the population variances are equal, you have to use a pooled variance t-test to construct the interval:

[(X[bar]₁-X[bar]₂) ± $t_{n_1+n_2-2;1-\alpha /2}$ * $Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }$ ]

$t_{n_1+n_2-2;1-/2}= t_{25;0.975}= 2.060$

$Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} }= \sqrt{\frac{11*529+14*576}{12+15-2} } = 23.57$

[(1000-1016)±2.060*23.57* $\sqrt{\frac{1}{12} +\frac{1}{15} }$ ]

[-34.80;2.80] mg

The 95% CI contains the value under the null hypothesis: "zero", so the decision is to not reject the null hypothesis. Then using a 5% significance level you can conclude that there is no difference between the average calcium content of supplements 1 and 2.

I hope it helps!

3 0

3 years ago