What is the half of 1.875 ? explain in detail ?

The required area under the curve of function v(t) is 195 square miles, which depicts the total distance traveled by car during the 3 hours.

The area under the curve of the function v(t) represents the total distance traveled by the car over the given time period.

The function v(t) is defined as the speed of the car (in miles per hour) at any given time t (in hours). Since the speed is constant at 65 miles per hour, the graph of v(t) will be a straight horizontal line at y = 65.

To find the distance traveled, we need to multiply the speed (in miles per hour) by the time (in hours):

Distance = Speed * Time

Following the given case, the speed is 65 miles per hour, and the car traveled for 3 hours:

Distance = 65 miles/hour * 3 hours = 195 miles

So, the area under the curve of v(t) is 195 square miles, which represents the total distance traveled by car during the 3 hours.

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(A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

The typical form for linear equations with two variables is Ax+By=C.

For instance, the linear equation 2x+3y=5 is in standard form.

So, we have the equation:

5x – 4y = 20

(A) (4,0)

=5x−4y

=5(4)−4(0)

=20

=RHS

(4,0): YES

(B) (0,5)

=5x−4y

=5(0)−4(5)

=−20

≠RHS

(0,5): NO

(C) (−2, 5/2)

=5x−4y

=5(−2)−4(5/2)

=−10−10

=−20

(−2, 5/2): NO

(D) (0, -5)

=5x−4y

=5(0)−4(−5)

=20

=RHS

(0, -5): YES

(E) (2, -5/2)

=5x−4y

=5(2)-4(-5/2)

=10+10

=20

=RHS

(2, -5/2): YES

Therefore, (A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.

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The u(1, 1, 2), v(2, 3, 1), and w(4, 5, 5) supplied vectors are linearly dependent.

A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.

As per the given information in the question,

The given vectors are:

u = (1, 1, 2)

v = (2, 3, 1) and,

w = (4, 5, 5)

If there are three scalars that are not all zero and that are dependent on a set of vectors (u, v, and w), they have been shown to be linearly dependent.

au + bv + cw = 0

⇒ a(1, 1, 2) + b(2, 3, 1) + c(4, 5, 5) = (0, 0, 0)

⇒ (a + 2b + 4c, a + 3b + 5c, 2a+ b + 5c) = (0, 0, 0)

So,

a + 2b + 4c = 0    (i)

a + 3b + 5c = 0    (ii)

2a+ b + 5c = 0     (iii)

From equation (i) and (ii)

b = -c

From equation (i)

a - 2c + 4c = 0

⇒ a = -2c

Let's assume that c = 1

So,

a = -2 and,

b = -1

Then, from the obtained values,

-2u - v + w = 0

As a result, there is a set of non-zero values for a, b, and c such that:

au + bv + cw = 0

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Answer:

r = .5 units  

Step-by-step explanation:

8.7 R is an improper  FRACTION of the 2 pi R of the entire circle ....set up a ratio:

8.7 / (2 pi)  =  3.9 / x       where x is the entire circumference measurement

x = 3.9 / (8.7 / (2 pi) )   = 2.82 units    

To find the radius    circumf = 2 pi r

                                     2.82 = 2 pi r      shows r = .5 units

6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is  -6x³ +4x² -4

Polynomial is minus six x cube plus four x square minus four.

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

6x³ -4x² +4 is the additive inverse of -6x³ +4x² -4

because -6x³ +4x² -4+6x³ -4x² +4=0

Hence, 6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4

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Any data collection whose metrics of central placement only have the letter A as a value.Mode and median

For any given data set, the mode and median are the two measures of central location that have just one value. The mode is the most commonly occurring value in a given data set, while the median is the middle value in the data set when it is sorted in order from least to greatest. The mean, on the other hand, is an average of all the values in the data set, and the standard deviation is a measure of how much the values in the data set differ from each other. So, the answer is A. Mode and median.

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Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.

What is typing speed?

How many words a person can correctly type in one minute. He types at a 60 wpm rate.

Given:

Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour.

We have to find how many paged he can type in one hour.

First to convert improper fraction 1 2/7 into a fraction.

⇒ [tex]1\frac{2}{7} = \frac{7*1+2}{7} = \frac{9}{7}[/tex]

So, Shawn can type 9/7 pages in 1/3 of an hours.

i hour = 3/3

So, Shawn can type

9/7 x 3/3 = 27/21 =  [tex]1\frac{6}{21}[/tex] pages in one hour.

Hence, Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.

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Answer:

The answer to you question is 18 and  20

18 and 20

Students who test positive face serious consequences, including letters to their parents,

Answer:

-3

Step-by-step explanation:

5 + ( -8 )

-8 - 5 = -3

so final answer: -3 because ( - 8 ) so the ( - ) would go on the answer

Answer: -3

Step-by-step explanation: It would be -3 because since we are adding a negative it would go toward the negative side. Also, it can be modeled as:

5 - 8

This would still = -3.

The Least-squares problem that has minimal norm can be given using factorization.

The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.

It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.

When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.

The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.

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The scatterplots shown can be matched to the corresponding correlation coefficients , which are as follows :
Scatterplot A : -0.56

Scatterplot B : -0.96

Scatterplot C : 0.92

Scatterplot D : 0.53

What is correlation coefficient?
Correlation coefficient is a numerical measure of the degree of relationship between two variables. It is used to measure how closely related two variables are, and whether one variable is a good predictor of the other. It is measured on a scale of -1 to 1, with -1 representing a strong negative correlation, 0 representing no correlation, and 1 representing a strong positive correlation. A correlation coefficient of 0 suggests that the two variables are completely unrelated, while a coefficient of 1 suggests that the two variables are strongly related. Correlation coefficients can help to identify patterns in data and can be used to predict future values.

Note the following facts :

Scatterplot that shows a trend that rises from left to your right shows a positive correlation between two variables.

Scatterplot that descends from left to left to right shows a negative correlation between two variables.

The farther away the data points are from each other the greater the value the value of correlation coefficient.

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Answer:

Perimeter of the square patch is 240 cm.

Step-by-step explanation:

If the perimeter of each rectangular piece is 48 cm, then the length of each side of each rectangular piece is 12 cm. When the rectangular pieces are arranged to form a square patch, the patch will have 5 rows and 5 columns of rectangular pieces. Since the rectangular pieces are identical, the length of each side of the square patch will be 5 times the length of one side of a rectangular piece. Therefore, the length of each side of the square patch will be 5 * 12 cm = 60 cm.

The perimeter of the square patch is the sum of the lengths of all four sides of the patch. Since all sides of the patch have the same length, the perimeter of the square patch will be 4 * 60 cm = 240

Answer:x=-5

Step-by-step explanation:

x2+10=0

0-10=-10

x2=-10

-10/2=-5

x=-5

Following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.

In mathematics, an integral assigns numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data.

Integration is the action of locating integrals.

So, the number of automobiles that cross an intersection each hour is:

r(t) = 400 + 800t - 120t²

Integration should be carried out to establish the number of cars traveling through the intersection between 6 am and 8 am.

[tex]\begin{aligned}\int_{t_1}^{t_2} r d t & =\int_0^2 400+800 t-120 t^2 d t \\& =\left[400 t+400 t^2-40 t^3\right]_0^2 \\& =400 \times 2+400 \times 2^2-40 \times 2^3 \\& =800+1600-320 \\& =2080\end{aligned}[/tex]

Therefore, following integration, we may estimate that between 6 and 8 am, 2080 automobiles will pass through the crossing.

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Correct question:
The traffic flow rate (cars per hour) across an intersection is r ( t ) = 400 + 800 t − 120 t 2 , where t is in hours, and t =0 is 6am. How many cars pass through the intersection between 6 am and 8 am?

Answer:

69.5ft²

Step-by-step explanation:

The shaded area is right triangles,

The formula for area of a right triangle is 1/2 x base x height

Triangle on right

Base: 7.6ft

Height: 10ft

Plug in: 1/2 x base x height = 1/2 x 7.6ft x 10ft = 38

Triangle on left

Base: 6.3ft

Height: 10ft

Plug in: 1/2 x base x height = 1/2 x 6.3ft x 10ft = 31.5

Add both for total shaded area: 31.5 + 38 = 69.5ft²

Probability of getting head = 0.45

Probability of getting tail = 1- 0.45

                                         = 0.55

No of flip flops = 10

The common ratio of the sequence which have first term, = 3 and third term  = 192 is calculated to be 6

The common ratio of the sequence is calculated by comparing the preceding terms as done below

first term = a = 3

second term = a * r = 3r

third term = second term * r

= a * r * r

= 3r * r

= 3r²

The given data shows that, third term = 192

3r² = 192

divide through by 3

3r² / 3 = 192 / 3

r² = 64

r = √64

r = 8

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In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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Answer:

630

Step-by-step explanation:

35% of 1800 = 0.35 × 1800 = 630

Answer:

nah

Step-by-step explanation:

Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  [tex]x = 12.7[/tex]

Population standard deviation of  [tex]\sigma = 6.37[/tex]

Sample size of .n = 50

The margin of error is:

[tex]M = z \frac{\sigma }{\sqrt{n} }[/tex]

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  [tex]\frac{1+\alpha }{2}[/tex] , in which  [tex]\alpha[/tex] is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

[tex]M= 1.96\frac{6.37}{\sqrt{50} } = 1.77[/tex]

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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The length of the side AB represented by x in the triangle ABC is equal to 16 using the trigonometric ratio of sine.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

The triangles ABC and ADB are right-angled triangles, we shall be considering the trigonometric ratio of the sine of angle A which is common to both triangles.

For triangle ABC;

sinA = adjacent/hypotenuse

sinA = x/32

for triangle ADB;

sinA = 8/x

thus we can say that;

x/32 = 8/x {cross multiplication}

x² = 3 × 32

x² = 256

x =√256 {take square root for both sides}

x = 16.

Therefore, 16 is the length of the side AB labelled x, using the trigonometric ratio of sine of the common angle A to the triangles ABC and ADB.

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Answer:

true false false true true

Step-by-step explanation:

I will help you sir.

Given

Opposite Sides are Congruent

Reflexive

SSS

CPCTC

The function simulates exponential decay, and it degrades by 5.1% for every increment in x.

Explosive increase and decay are common in situations where quantities change rapidly. It has been suggested that exponential development and decay follow a geometric progression. Quantities that change exponentially rather than continually are referred to be exponentially growing or decaying.

As per the given data in the question,

An exponential function with the formula y = a[tex]r^x[/tex] is the function that is given.

a = 330

r = 0.949

The function indicates exponential growth if the base r is larger than 1. The function shows exponential decline if indeed the base r is far less than 1. In this instance, the function depicts exponential decline because the base r is smaller than 1, or 0.949.

If we want to describe the rate of reduction as a percentage, we can remove the base r by 1 and multiply it by 100.

The rate of reduction as a percentage in this instance is:

1 - 0.949 = 0.051 ×100

= 5.1%.

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Answer: x= 4/9

Step-by-step explanation:

9x^2-16=0

9x^2 = 16

9x = 4

x= 4/9

The money in the account at the end of the 4 years is $1034

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Now we are given that the initial amount deposited in the account is $1000

This account is giving 0.85% And we have to figure out how much amount will be there

We use compound interest formula to find the amount

[tex]A= P(1+r/n)^{nt}\\\\A= 1000(1+0.0085)^{4}\\A = 1000(1.034)\\A= 1034[/tex]

Hence the amount will be after 4 years is $1034.

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