If log103 0.4771,
evaluate log100.0003.
Round your answer to four decimal
places.

Did not understand "full working pliz".

Answer:

6%

Step-by-step explanation:

Got it right on the test.

Answer: [tex]\Large\boxed{3.52~;~66.88}[/tex]

Step-by-step explanation:

Given information

One number is 19 times the other

The smaller number is less than 5

Sum = 70.4

Set variables

Let x be the smaller number

Let 19x be the larger number

Set equation according to the given information

Smaller number + Larger number = Sum

x + 19x = 70.4

Simplify by addition

20x = 70.4

Divide 20 on both sides

20x / 20 = 70.4 / 20

[tex]\Large\boxed{x=3.52}[/tex]

Substitute values into the variables to find the larger number

Larger number = 19x

                         = 19 (3.52)

                         [tex]\Large\boxed{=66.88}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

smaller number 3.52

greater number 66.88

Step-by-step explanation:

Let x and y be two numbers ,where x < 5 and x ≤ y.

x + y = 70.4

y = 19x

By replacing y by 19x in the first equation we get :

x + 19x = 70.4

Then

20x = 70.4

Then

x = 70.4÷20

  = 3.52

y = 19x

Then

y = 19 × 3.52  (just replace x by 3.52)

  = 66.88

The child is 59.4 inches tall, assuming the length from the coach's shoulder to his head cap is approximately 10 inches.

Height refers to the vertical distance between the top and bottom of something.

Height measures the length of some objects or persons vertically to determine whether it is high or low, according to some ascertained criteria.

Baseball coach's height = 70 inches

Coach's shoulder to head = 10.6 inches

Height of the child standing slightly below the coach's shoulder = 59.4 inches (70 - 10.6)

Thus, the child standing slightly below the coach's shoulder is 59.4 inches tall.

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Assume that the height of the coach from his shoulder to the head is 10.6 inches.

We should combining 8 ounces of the 50/50 nuts with 8 ounces of the 80% chocolate-covered nuts, to create the 60% mixture required for each bag.

You are offering to assist with the Valentine's Day fundraiser for the soccer team, according to the query. At least 60% of the 16-ounce bags of nuts that the team sold had to be coated in chocolate.

However, they supplied two sizable containers of mixed nuts instead of a shipment that was divided into plain and chocolate nuts. First, it claims to be equally split between plain and chocolate-covered. The second one has almonds that are 80 percent chocolate-covered.

In order to create the 60% mixture required for each bag, we should combine 8 ounces of the 50/50 nuts with 8 ounces of the 80% chocolate-covered nuts.

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To make the 60 percent mixture needed for each bag, we should combine 8 ounces of the 50/50 nuts with 8 ounces of the 80 percent chocolate-covered nuts.

According to the question, you are willing to help with the Valentine's Day fundraiser for the soccer team. The team had to cover at least 60% of the 16-ounce bags of nuts they sold in chocolate.

Instead of a cargo that was split into plain and chocolate nuts, they instead provided two substantial containers of mixed nuts. First, it asserts that the basic and chocolate-covered portions are split equally. The second one has almonds that have been wrapped in 80 percent chocolate.

We need to combine 8 ounces of the 50/50 nuts with 8 ounces of the 80% chocolate-covered nuts.to make the 60 percent combination needed for each bag.

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a) [tex]\angle QST[/tex]

b) Arc QT

c) Arc QRS

d) 105 degrees

e) 255 degrees

g(x) is a translation of 6 units downwards.

Here we have the function:

y = f(x) = 3x + 1

Notice that the y-intercept of f(x) is:

f(0) = 3*0 + 1 = 1

The y-intercept of f(x) is y = 1.

Now, we know that the y-intercept of g(x) is -5. then:

g(x) = 3x - 5 = f(x) - 6

Meaning that g(x) is a translation of 6 units downwards.

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Answer:

translated 2

units up

g(x)= f(x-2)

Step-by-step explanation:

Answer:

No classification is guaranteed.

The graph is shown in the attached image.

Based on the number of students at Roxas Middle School and the number of students studying Chinese and Spanish, the number of students who study Spanish is 182 students.

The first thing to do is to find out the number of students who are studying either Spanish or Chinese:

= Total number of students - Students studying both Spanish and Chinese

= 374 - 100

= 274 students

Then, assuming the number of students studying Chinese alone is x, the expression to find them would be:

274 = 2x + x

Solving gives:

2x + x = 274

3x = 274

x = 274 / 3

x = 91 students

The number studying Spanish is twice this number so will be:

= 91 x 2

= 182 students

In conclusion, there are 182 student studying Spanish.

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Answer:

the coordinates of equations

1.4x+y=-7

for x =0

f(0,y)=4(0)+y=-7

y=-7

for y=0

f(x,0)=4x+0=-7

4x=-7

x=-7/4

2.x-y=2

for x=0

f(0,y)=0-y=2

-y=2

y=-2

for y=0

f(x,0)=x-0=2

x=2

graph all of the equations coordinates or you can look the image

so the answers are : {-3,-1}

CMIIW

Answer: No

Step-by-step explanation:  proportional means corresponding in size or amount to something. However, the number of her sit-ups isn't consistent, so it isn't proportional to the time she spends doing them.

[tex]y = 5x \\ switch \: y \: and \: x \\ x = 5y \\ solve \: for \:y \\ y = \frac{x}{5} [/tex]

Grandma should be able to make three slices of French toast by slicing one of the original slices into two.

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Separating variables, we have

[tex]\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx[/tex]

Integrate both sides.

[tex]\displaystyle \int y\,dy = \int x\,dx[/tex]

[tex]\dfrac12 y^2 = \dfrac12 x^2 + C[/tex]

Given that [tex]y(0)=-1[/tex], we find

[tex]\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12[/tex]

Then the particular solution is

[tex]\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12[/tex]

[tex]y^2 = x^2 + 1[/tex]

[tex]y = \pm\sqrt{x^2 + 1}[/tex]

and because [tex]y(0)=-1[/tex], we take the negative solution to accommodate this initial value.

[tex]\boxed{y(x) = -\sqrt{x^2+1}}[/tex]

Answer:

isosceles trapezoind

Step-by-step explanation:

An isosceles trapezoid is a trapezoid with congruent base angles.

Mathematically speaking, the Riemann sum of the linear function is represented by A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}, whose representation is represent by the graph in the lower left corner of the picture.

Graphically speaking, Riemann sums with right endpoints represent a sum of rectangular areas with equal width with excess area for positive y-values and truncated area for negative y-values generated with respect to the x-axis. Mathematically speaking, this case of Riemann sums is described by the following expression:

A ≈ [(b - a) / n] · ∑ f[a + i · [(b - a) / n]], for i ∈ {1, 2, ..., n}

Where:

a - Lower limit

b - Upper limit

n - Number of rectangles

i - Index of a rectangle

If we know that f(x) = 2 · x - 1, a = - 6, b = 4 and n = 5, then the Riemann sum with right endpoints of the area below the curve is:

A ≈ [[4 - (- 6)] / 5] · ∑ 2 [- 6 + i · [[4 - (- 6)] / 2]] - [[4 - (- 6)] / 5] · ∑ 1, for i ∈ {1, 2, 3, 4, 5}

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Answer:

show the image because we cant answer it if there's no picture or image

Step-by-step explanation:

Step-by-step explanation:

1.

the expected sample mean is always the general mean : 168.5 pounds.

2.

the SD of a sample is the general SD / sqrt(sample size).

in our case

the sample SD = 68/sqrt(150) = 5.55217675...

3.

if we are looking for only the probability that any single woman is below 160 pounds, we would use the normal z calculation :

z = (x - mean)/SD = (160 - 168.5)/68 = -8.5/68

but we have here the question about the probability of the mean value of a whole sample of 150 women.

so, we need to adapt the z-calculation by the principle of 2) for the SD of a sample :

z = (x - mean)/(SD × sqrt(sample size)) =

= (160 - 168.5)/(68 × sqrt(150)) = -8.5/(68×sqrt(150)) =

= -0.010206207 ≈ -0.01

that gives us in the z-table the p-value 0.49601

this 0.49601 is the probability that a sample of 150 women has a mean value of below 160 pounds.

4.

similar to 3.

the z value we are looking for

z = (175 - 168.5)/(68 × sqrt(150)) = 6.5/(68 × sqrt(150)) =

= 0.007804747... ≈ 0.01

that gives us the p-value 0.50399.

that would be the probability of a sample mean of 175 or below.

to get above 175 we need to get the other side of the bell-curve :

1 - 0.50399 = 0.49601

so, this case has about the same probability as 3.

5.

as 3), just with the sqrt(200) instead of the sqrt(150).

z = -8.5/(68 × sqrt(200)) = -0.008838835... ≈ 0.01

so, the probability is still about the same as in 3) :

0.49601

6.

as 4) just with sqrt(200).

z = 6.5/(68 × sqrt(200)) = 0.006759109... ≈ 0.01

so, the probability is still about the same as for 4) :

0.49601

The answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

What is probability ?

Probability is a measure of the likelihood of event to occur. The probability of all the events in a sample space adds up to 1.

1)

We know that the expected mean of a sample is always equal to general mean.

As per the question, mean weight is 168.5 pounds.

This implies :

The expected mean for a sample of 150 women is :

= 168.5 pounds

2)

The standard deviation (SD) of the mean for a sample of 150 women is :

= 68 / (√150)

= 5.55

3)

The probability of 150 women having a sample mean below 160 pounds will be represented by z and will be :

z = ( x - mean) / ( SD × (√sample size))

= (160 - 168.5) / (68 × √150)

= 0.01

If we use the z table then the probability will be :

= 0.49601

4)

Similarly as part 3 :

z = (175 - 168.5) / (68 × √150)

z  = 0.01 (approximately)

The probability of 150 women having a sample mean below 175 pounds will be :

= 0.50399

And the probability of 150 women having a sample mean above 175 pounds will be :

= 1 - 0.50399

= 0.49601

5)

Here , we have to find probability of 200 women , so 150 in formula of z in 3rd part will be replaced by 200.

i.e.,

z = (160 - 168.5) / (68 × √200)

z = 0.01 ( approximately)

and probability will be :

= 0.49601

6)

Here , we have to find probability of 200 women , so 150 in formula of z in 4th part will be replaced by 200.

z = (175 - 168.5) / (68 × √200)

z = 0.01

And probability equal to :

= 0.49601

Therefore , the answers are :

1) The expected mean for a sample of 150 women is 168.5 pounds.

2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.

3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.

4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.

5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.

6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.

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The FOIL method is a method of expanding two given brackets by following the required steps. Thus using the FOIL method, the required answer is: -7

Expansion of brackets may be done using different methods, but these methods would give the same answer. Some methods that can be used are the binomial expansion method, FOIL method, etc.

The FOIL method is a shortened form of the steps required for the process. These required steps are First, Outside, Inside, and last.

Thus to expand the given brackets in the question, we have;

(5+2)(4-5) = 5(4 - 5) + 2(4 - 5)

                = 20 - 25 + 8 - 10

                = 28 - 35

(5+2)(4-5) = -7

Thus using the FOIL method, the answer to the question is -7.

Quick check: (5+2)(4-5) = (7)(-1)

                             = -7

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We want to find [tex]x[/tex] such that

[tex]\mathrm{Pr}(X \le x) = 0.81[/tex]

where [tex]X[/tex] is the random variable for test scores, and [tex]X\sim\mathrm{Normal}(63,9.3^2)[/tex].

Transform [tex]X[/tex] to [tex]Z\sim\mathrm{Normal}(0,1)[/tex] using the relation

[tex]X = \mu + \sigma Z \implies Z = \drac{X-63}{9.3}[/tex]

so that

[tex]\mathrm{Pr}(X \le x) = \mathrm{Pr}\left(\dfrac{X-63}{9.3} \le \dfrac{x-63}{9.3}\right) = \mathrm{Pr}\left(Z \le \dfrac{x-63}{9.3}\right) = 0.81[/tex]

Applying the inverse CDF of [tex]Z[/tex] (denoted by [tex]\Phi^{-1}[/tex]), we have

[tex]\dfrac{x-63}{9.3} = \Phi^{-1}(0.81) \approx 0.8779[/tex]

Solve for [tex]x[/tex].

[tex]\dfrac{x-63}{9.3} \approx 0.8779[/tex]

[tex]x-63 \approx 8.1644[/tex]

[tex]x \approx 76.1644[/tex]

Then the cutoff test score for the 81% percentile is [tex]P_{81} \approx \boxed{76}[/tex].

Answer:

Answer is c, 67.

Step-by-step explanation:

So angle L and K are going to be the same, and so its going to be:

46+2n=180, since 180* inside a triangle and n= both L and K.

180-46=134

134/2=67

Both K and L will be 67.

Answer is c, 67.

To check, 46+67+67=180

The measure of angle JLK is 67 degree.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The angle L and K are going to be the same;

46+2n=180,

Since 180 inside a triangle and n= both L and K.

180-46=134

134/2=67

Both K and L will be 67.

The answer is c, 67.

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The value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

The equation is given as:

(43/7 ÷ x + 32/9) ÷ 25/6 = 4/3

Rewrite as a product

(43/7 ÷ x + 32/9) x 6/25 = 4/3

Multiply both sides of the equation by 25/6

(43/7 ÷ x + 32/9)= 4/3 x 25/6

Evaluate the product

(43/7 ÷ x + 32/9)= 50/9

Rewrite the equation as:

43/7x + 32/9= 50/9

Subtract 32/9 from both sides

43/7x = 2

Multiply both sides by 7x

14x = 43

Divide by 14

x =43/14

Hence, the value of x in the equation (43/7 ÷ x + 32/9) ÷ 25/6 = 4/3 is 43/14

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Answer:

40 meters a minute

Step-by-step explanation:

800m - 20 min

800/20

40m-1 min

Answer:

  x-intercept: (4, 0)

  y-intercept: (0, 3)

Step-by-step explanation:

The intercepts of the equation can be found by setting each variable to zero and solving for the other. The graph will be a line through the intercept points.

Setting x=0 and solving for y, we have ...

  4y -12 = 0   ⇒   y = 12/4 = 3

Setting y=0 and solving for x, we have ...

  3x -12 = 0   ⇒   x = 12/3 = 4

The intercepts are ...

  x-intercept: (4, 0)

  y-intercept: (0, 3)

The line will go through these intercept points.

Answer:

k ≈ 50.77

Step-by-step explanation:

using the cosine ratio in the right triangle

cos19° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{48}{k}[/tex] ( multiply both sides by k )

k × cos19° = 48 ( divide both sides by cos19° )

k = [tex]\frac{48}{cos19}[/tex] ≈ 50.77 ( to 2 dec. places )

Hi :)

            We'll use sohcahtoa to solve this problem

[tex]\Large\boxed{\begin{tabular}{c|1} \sf{Sohcahtoa} ~&~~~~~Formula~~~~~~~ \\ \cline{1-2} \ \sf{Soh} & Opp~\div \text{hyp}\\\sf{Cah} & Adj \div \text{hyp}\\\sf{Toa} & Opp \div \text{adj} \end{tabular}}[/tex]

Looking at our triangle, we can clearly see that we have :

Set up the ratio

[tex]\longrightarrow\darkblue\sf{cos(19)=\dfrac{48}{k}}[/tex]

solve for k

[tex]\longrightarrow\darkblue\sf{k\cos(19)=48}[/tex] > multiply both sides by k to clear the fraction

[tex]\longrightarrow\darkblue\sf{k=\dfrac{48}{\cos(19)}}[/tex]  > divide both sides by cos (19)

[tex]\star\longrightarrow\darkblue\sf{k\approx50.77}\star[/tex]

[tex]\tt{Learn~More ; Work\ Harder}[/tex]

:)

Step-by-step explanation:

68% of all values are within 1 SD (110 ± 15).

95% of all values are within 2SD (110 ± 2×15 = 30)

99.7% of all values are within 3 SD (110 ± 3×15 = 45)

a)

95 is 110 - 15, so exactly 1 SD apart from the mean value.

68% or 0.68 is the probability of all values between 95 and 125.

so, 34% or 0.34 is the probability of all values between 95 and 110. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 95 is

0.34 + 0.5 = 0.84

b)

125 is 110 + 15, so exactly 1 SD apart from the mean value.

so, as per a) 34% or 0.34 is the probability of all values between 110 and 125. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 125 is

0.5 - 0.34 = 0.16

Answer:

(3+3) x (3+1)

Step-by-step explanation:

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

Answer: C

Step-by-step explanation:

We can use the expanding rule to get that one if the expressions is

(9x^2 + 2x - 7)x + (9x^2 + 2x - 7)(-4)

Check the picture below.

so the composite is really a trapezoid and two triangles, let's get their area and sum them all up.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a = 2\\ b = 5\\ h = 7 \end{cases}\implies A=\cfrac{7(2+5)}{2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{yellow~trapezoid}{\cfrac{7(2+5)}{2}}~~ + ~~\stackrel{blue~triangle}{\cfrac{1}{2}(\stackrel{b}{3})(\stackrel{h}{5})}~~ + ~~\stackrel{orange~triangle}{\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{2})}} \\\\\\ 24.5~~ + ~~7.5~~ + ~~10\implies \text{\LARGE 42}[/tex]