This is for math nation unit 1 please help!!

Answer:

19cm

Step-by-step explanation:

I think it's 19cm as sides BC on the green triangle measure 15cm, and EF is 25cm on the blue triangle. It also mentions that they are similar, meaning that ∆ DEF is just a translated and enlarged version of ∆ ABC

25 - 15 = 10cm

9 + 10 = 19cm

Hope this helped :)

The median number of students who checked books out of the library in a 10-day period is 50.

We have,

To find the median of the list, we need to first put the numbers in order from least to greatest:

32, 35, 40, 40, 48, 52, 63, 68, 75, 83

The median is the middle value in the list.

If there is an odd number of values, the median is the middle value.

If there is an even number of values, the median is the average of the two middle values.

There are 10 values, which is an even number.

The middle values are 48 and 52.

Median = (48 + 52) / 2

Median = 50

So the median number of students who checked books out of the library in a 10-day period is 50.

Interpretation:

The median represents the middle value in the list, which in this case is 50.

This means that half of the values in the list are greater than 50, and half of the values are less than 50.

In terms of the number of students checking out books, this means that 50 is the typical number of students who checked books out of the library during the 10-day period.

Thus,

The median number of students who checked books out of the library in a 10-day period is 50.

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Answer:6

Step-by-step explanation: It’s 6 because it’s only greater than, not greater than or equal to

a) The 99% confidence interval for the proportion of all caterpillars that lived to become a butterfly is between 0.078 and 0.166.

b) About 99% of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The sample size and the estimate for this problem are given as follows:

[tex]n = 369, \pi = \frac{45}{369} = 0.122[/tex]

The lower bound of the interval is given as follows:

0.122 - 2.575 x sqrt(0.122 x 0.878/369) = 0.078.

The upper bound of the interval is given as follows:

0.122 + 2.575 x sqrt(0.122 x 0.878/369) = 0.166.

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The number shown is not written in scientific notation because the 10 do not raise to power of any number, and exponential on the second value do not represent a particular power.

Scientific notation  can be described as the way of writing very large  as well as very small numbers.

It should be noted that the  number is written in scientific notation which is been done as a result of the number falling between 1 and 10 and then this number is been multiplied by a power of 10 instance of this is 6.5 ✕ 10^8, then we can see that none of the given values have the sa,me expresion with this example.

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The option that best describes the change in viewers the network is experiencing is B. Each year, the total number of viewers increases to approximately 120% of the previous year's total.

When 't' surpasses 1/ln(5) at 3.5, the expression yields a negative result; connoting the network is witnessing a dwindling viewership.

Consequently, the network initially experiences an intensifying viewership ratio which then fades; in accordance with Option B, "Each year, the total number of viewers increases to roughly 120% of the preceding year's sum". Clearly, this demarcation reveals itself as the accurate answer.

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The likelihood that Mia and Lia place in 1st or 2nd is unlikely

From the question, we have the following parameters that can be used in our computation:

People = 50

Positions = 1st, 2nd, and 3rd place

The probabilities are

P(1st) = 1/50

P(2nd) = 1/49

Using the above as a guide, we have the following:

P = 1/50 * 1/49

Evaluate

P = 0.00040816326

This value is less than 50%

So, the likelihood is unlikely or less likely

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The mass per running metre of a copper bar with a uniform cross-section in the form of a triangle as shown in the figure when the density of copper is 8 850 kg/m³ is 3.

Mass per running meter = density x area x length

Substituting the values for density, area, and length, you get:

Mass per running meter = 8,850 x [(b x h) / 2] x length

Simplifying the equation, you get:

Mass per running meter = 4,425 x b x h x length

Mass = 8850 / 4425

Mass = 2

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↬ x² - 6x -5

Substituting x = 3:-

⟶ x² - 6x -5

⟶ (3)² - 6(3) -5

⟶ 9 - 6 × 3 - 5

⟶ 9 - 18 - 5

⟶ 9 - 23

⟶ -14

Answer:

[tex] \gg{ \underline{ \large \: \boxed { \bf {- 14}}}}[/tex]

Step-by-step explanation:

[tex] \large \: \sf { \underline{Given}}[/tex]

[tex] \large \sf \underline{Solution }[/tex]

[tex] \large \: \displaystyle \sf {x}^{2} - 6x - 5[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \large \bf \blue{ \underline{putting \: the \: value \: of \: x}}[/tex]

[tex]\large \: \displaystyle \sf \: {3}^{2} - 6(3) - 5 [/tex]

[tex]\large \: \displaystyle \sf \: = \: 9 - 18 - 5[/tex]

[tex]\large \: \displaystyle \sf \: = \: - 9 - 5[/tex]

[tex]\large \: \displaystyle \bf \red{= - 14}[/tex]

The completed calculation with regards to the area of the congruent triangles can be presented as follows;

The distance formula indicates;

AM = √((x₂ - x₁)² + (y₂ - y₁)²)

Therefore, we get;

AM = √((4 - 0)² + (0 - 0)²) = √(4²)

AM = √(4²) = 4

BM = √((x₂ - x₁)² + (y₂ - y₁)²)

BM = √((4 - 4)² + (6 - 0)²) = √(6²)

BM = √(6²) = 6

AM ≅ CM Definition of the midpoint of AC

AM = CM Definition of congruent segments

CM = 4 Substitution property

Area ΔABM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Area ΔCBM

A = (1/2)·b·h

= (1/2) × 4 × 6

= 12

Therefore Area ΔABM = area ΔCBM by congruence

Triangles are congruent if they have the same size and shape.

The details of the reasons for the calculation steps and values are presented as follows;

Definition of midpoint of a segment

The midpoint of a line segment is the point that divides the segment into two parts of the same length

Definition of congruence?

Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement

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Answer:

B always because a rectangle has two sets of parallel sides

Hope this helps

Answer:

n₁ = 198,610

P₁ = 27/198,610

n₂ = 196,877

P₂ = 104/196,877

q₁ = 1 - P₁

q₂ = 1 - P₂

Step-by-step explanation:

Answer:

19.5625

Step-by-step explanation:

[tex]\frac{2(12) + 4(15) + 16 +18 + 2(20) + 22 +3(25) +2(29)}{16}[/tex] = [tex]\frac{313}{16}[/tex] = 19.5625

We add up all the numbers that are represented on the graph and then divide that by 16 because there are 16 numbers.

Helping in the name of Jesus.

The statements that defines the term resources is A. materials that help you achieve your goals.

Resource  can be described as all the materials available  that is available in individual environment  and can be seen as one that is  technologically accessible.

It should be noted that resources do help us to achieve most of our goals and can be seen as one that is economically feasible  as welll as culturally sustainable and they serves as things that can help us and thjat can  satisfy our needs and wants which is needed on daily basis.

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The solution is, : the area of the rectangle is 4000 sq inches.

Here, we have,

A rectangle is given with sides 82 and 48 inches

We have to round off these dimensions to the nearest 10.

82 inches ~80 inches

since 2 <5, we make it 0

Similarly 48 inches ~50 inches since 8>5

Now area

= length x width

=80(50)

=4000 square inches

Hence, the area of the rectangle is 4000 sq inches is correct answer.

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Answer:

$814 she kept for 5 years if she don't spend it

Step-by-step explanation:

Based on my experiment, My appropriate conclusion based on the results  is option A: The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.

This conclusion is based on the truth that the experiment  conducted in California found that 85% of the respondents matches with the view,  one that is diverse from the extent of Modern York inhabitants (88%) who concurred with the same conclusion .

The "strong evidence" based on the experiment shows that the findings are statistically significant and the conclusion will thus be that the extent of California inhabitants who agree is "essentially wide" from the extent of other York inhabitants, showing some differences between the two populaces.

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The value of the term a5 is 39

From the question, we have the following parameters that can be used in our computation:

{3, 12, 21, 30, 39, 48, 57}

The expression a5 means the 5th term of the sequence

In {3, 12, 21, 30, 39, 48, 57} , the fifth eterm is 39

Hence, a5 = 39

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Answer:

Step-by-step explanation:

Answer:

28.27 CM ^2

Step-by-step explanation:

The formula for area of a circle is pi * r^2 where r = the radius.

Plugging the radius into the formula we get pi3^2, which equals 28.274 cm ^2 (and change)

Answer: B: [tex]\sqrt{65}[/tex]

Step-by-step explanation:

The figure indicates this is a right triangle. As such, we can use the pythagorean theorem:

a^2 + b^2 = c^2

16 + 49 = x^2

sqrt(65) = x

.: x = [tex]\sqrt{65}[/tex]

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_3(N)=x\implies 3^x=N[/tex]

To convert 5.4 square meters to square centimeters is 54,000 cm²

To convert 5.4 square meters (m²) to square centimeters (cm²),

We need to multiply it by 10,000 (since 1 meter = 100 centimeters).

5.4 m² = 5.4 x 10,000 cm² = 54,000 cm²

Therefore, 5.4 square meters is equal to 54,000 square centimeters.

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Answer:

5/36

Step-by-step explanation:

hope this helps

The true statement about the graphs:

Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x).

The correct answer is an option (C)

First we draw a graph of function f(x) = -x + 3.

Find the graph in attached figure.

the x-intercept of f(x) is:

0 = -x + 3

i.e., x-intercept = (3, 0)

Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3.

Let g(x) = -1(-x + 3)

The x-intercept of g(x) would be,

0 = -1(-x + 3)

i.e., x-intercept = (3, 0)

Let h(x) = -2(-x + 3)

The x-intercept of h(x) would be,

0 = -2(-x + 3)

2x = 6

i.e., x-intercept = (3, 0)

Let t(x) = -3(-x + 3)

The x-intercept of t(x) would be,

0 = -3(-x + 3)

3x = 9

i.e., x-intercept = (3, 0)

the graph of functions g(x), h(x) and t(x) is shown below.

We can observe that the x-intercept is same for all graphs but the slopes are different.

Therefore, the correct answer is an option (C)

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The probability that the total team time in the 400-meter freestyle relay is less than 215 seconds is: 0.8345

From the table given the mean and standard deviation, we can say that:

Total time spent = 54.2 + 57 + 55.3 + 53.7

Total time spent = 220.2 secs

The total standard deviation is:

2.8 + 3 + 2.4 + 2.5 = 10.7 secs

Formula for z-score here is:

z = (x' - μ)/(σ/√n)

where:

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

Thus:

z = (220.2 - 215)/(10.7/√4)

z = 0.972

From online p-value from z-score calculator, we have:

p(x < 0.972) = 0.8345

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Answer: b

Step-by-step explanation: cause i just did it

The rate of interest with the given amount and compound interest is 5 percent.

Given that,

After 1 year: compound interest = $30 and total amount=$630.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Here, principal = 630-30=600

630=600(1+r/100)¹

630/600 = 1+r/100

1.05=1+r/100

1.05-1=r/100

0.05=r/100

r=5%

Therefore, the rate of interest with the given amount and compound interest is 5 percent.

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Answer:

Step-by-step explanation:

You want solutions to the equation 4sin(θ)² -7sin(θ) -4 = 0 on the interval [0, 2π].

A graph of the left-side expression shows it has a value of 0 at ...

  θ ≈ 3.61 or 5.81.

Using a calculator to check the offered answer choices, we find the values of θ that best satisfy the equation are θ = 3.61 or 5.81. (For this purpose, ±0.02 ≈ 0.)

We can let x = sin(θ). Then the equation is ...

  4x² -7x -4 = 0

  x² -7/4x = 1

  (x -7/8)² = 1 +(7/8)² = 113/64

  x = (7 ±√113)/8

The value (7+√113)/8 is greater than 1, so the only value of x that is useful here is x = (7-√113)/8. The angles in the desired range are ...

  {π - arcsin((7 -√113)/8), 2π +arcsin((7 -√113)/8)} ≈ {3.61, 5.81} . . . radians

2. The side AC corresponds to side AE of the other triangle.

3. The length of side BC is 15.

Two or more triangles are said to be similar if on comparing their properties, there exist some common relations. Some of the common relations are; measure of internal angles, scale factor etc.

From the diagram given, we have;

2. Given that the triangles are similar, thus:

The side AC corresponds to side AE of the other triangle.

3. On comparing the corresponding length of the triangles, we have;

15/ 25 = 9/ BC

15BC = 9 x 25

         = 225

BC = 225/ 15

     = 15

The length of side BC is 15.

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