Raj tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Find the present ages of Raj and his daughter. Also, verify the present age of Raj and his daughter graphically

Answer:

x> 1/6

Step-by-step explanation:

-2(8x – 4)< 2x + 5

Distribute

-16x +8 < 2x+5

Add 16x to each side

-16x +8+16x < 2x+16x+5

8 < 18x+5

Subtract 5 from each side

8-5 < 18x

3 < 18x

Divide each side by 18

3/18 < 18x/18

1/6 < x

Answer:

\(x > \frac{1}{6} \)

First answer is correct.

Step-by-step explanation:

\( - 2(8 x - 4) < 2x + 5 \\ - 16x + 8 < 2x + 5 \\ - 16x - 2x < - 8 + 5 \\ - 18x < - 3 \\ \frac{ - 18x}{ - 18} < \frac{ - 3}{ - 18} \\ x > \frac{1}{6} \)

Answer:

3π, 6π

Step-by-step explanation:

12π*1/4=3π

16π*135/360=6π

the length of arc:

\(\tt =\dfrac{\alpha }{360}\times 2\pi.r\)

5.

\(\tt \dfrac{90}{360}\times 2\pi6= 3\pi~yd\)

7.

\(\tt \dfrac{135}{360}\times 2\pi.8=6\pi~km\)

Answer:

heyy matee...

going according to given parameters

let 2 numbers be x and y

so atq =>

3x + y = 142 => y = 142 - 3x

and 4x - y = 148

4x - ( 142 - 3x ) = 138

4x - 142 + 3x = 138

7x = 280

x = 40

now y = 142 - 3(40) = 142 - 120 = 22

so x = 40 and y = 22

Answer:

Hope so, it helped you.

Step-by-step explanation:

For solving the equation i elimanated y by adding both the equation.

The number of followers Rita has is 13086.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of followers Rida has = 6,218

92 people stop following Rida's blog.

This means,

6218 - 92 = 6126

417 people start following Rida's blog.

This means,

6126 + 417 = 6543

The number of followers doubles.

This means,

6543 x 2 = 13086

Thus,

The number of followers Rita has is 13086.

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Katie outscored approximately 1.39% of the students in her section.

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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Answer:

51,000

Step-by-step explanation:

Answer:

v >=18

Step-by-step explanation:

Really don't know how to explain it

The term central location or central tendency relates to the way data tend to cluster around some middle or central value

It is a number located towards the center of the distribution of the values of a series of observations, that are called measures, in which the set of data is located. The most commonly used measures of central tendency are: mean, median and mode.

Statistics is a branch of mathematics that allows you to collect, organize and analyze data according to the need you have, for example: to obtain a result, compare information, make better decisions, among many other things.

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Answer:

Let the Distance traveled by car = X miles

Then amount of gas consumed= Y gallons

As car travels more distance, amount of gas consumption will increase.

So,⇒Amount of gas Consumption=k×  Distance traveled by car

Where k is sign of proportionality.

⇒Y = k X

This is equation in two variable of a line passing through the origin.

Drawn the Graph for you below

If X=1, Y=1

then k=1/1=1

If X=2, Y=2, then k=1

It shows uniform motion of car.

Step-by-step explanation:

The symbol used to denote the f-value having area is the F-statistic or F-value. This is typically represented by the letter "F" followed by specific subscript values.

The F-statistic is a ratio of two variances that follows an F-distribution when the null hypothesis is true. It is used in various statistical tests, such as the analysis of variance (ANOVA), to compare the means of different groups. Here's a step-by-step explanation:

1. Calculate the variances: For each group, find the variance (the average of the squared differences from the mean). The larger variance will be placed in the numerator, while the smaller variance will be placed in the denominator.

2. Compute the F-statistic: Divide the larger variance by the smaller variance. This results in the F-value, which follows an F-distribution.

3. Determine the degrees of freedom: The degrees of freedom (df) for the numerator and denominator are determined based on the sample sizes of the groups being compared. The numerator df is equal to the number of groups minus one, while the denominator df is equal to the total number of observations minus the number of groups.

4. Consult the F-distribution table: With the calculated F-value and degrees of freedom, you can consult an F-distribution table to determine the critical value or the p-value.

5. Make a decision: Compare the calculated F-value to the critical value or the p-value to the significance level. If the F-value is greater than the critical value or the p-value is less than the significance level, you can reject the null hypothesis, indicating that there is a significant difference between the group means.

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a.The probability that a randomly selected watch will be in working condition for more than five years is approximately 6.68%. b.Approximately 93.32% of the watches will be in operating condition after the warranty period. c. The maximum life expectancy of the middle 95% of the watches is approxiamately 63.68 months. d.The range of the middle 95% of the watches is from 32.32 months to 63.68 months. The range represents 95% of the watches, it means that 5%.

a. To find the probability that a randomly selected watch will be in working condition for more than five years, we need to convert the time to the same unit as the distribution. Since the mean is given in years and the standard deviation is given in months,

we need to convert five years to months.

Mean = 4 years = 4 x 12 months = 48 months

Standard deviation = 8 months

To calculate the probability, we need to find the area under the normal distribution curve to the right of 60 months (5 years).

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to 60 months:

z = (x - μ) / σ

z = (60 - 48) / 8 = 12 / 8 = 1.5

The probability can be found by looking up the z-score in the standard normal distribution table or using a calculator. From the table or calculator, we find that the probability is approximately 0.0668, or 6.68%.

b. The warranty period for Timely brand watches is three years. To find the percentage of watches that will be in operating condition after the warranty period, we need to find the probability that a randomly selected watch will last longer than three years.

We need to convert three years to months:

Warranty period = 3 years = 3 x 12 months = 36 months

We calculate the z-score:

z = (x - μ) / σ

z = (36 - 48) / 8 = -12 / 8 = -1.5

Using the standard normal distribution table or a calculator, we find the area to the left of -1.5 is approximately 0.0668. The probability that a randomly selected watch will not last longer than three years is approximately 0.0668.

To find the percentage of watches that will be in operating condition after the warranty period, we subtract this probability from 1 (since we want the complementary probability):

Percentage = 1 - 0.0668 = 0.9332 = 93.32%

c. The middle 95% of the watches represents the range within which 95% of the watches' life expectancy falls. To find the minimum and maximum life expectancy of this range, we need to determine the z-scores that correspond to the cumulative probability of 0.025 and 0.975.

For the minimum life expectancy (lower bound), we look up the z-score that corresponds to a cumulative probability of 0.025. This z-score is approximately -1.96.

z = -1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (-1.96 * 8) = 48 - 15.68 = 32.32

The minimum life expectancy of the middle 95% of the watches is approximately 32.32 months.

For the maximum life expectancy (upper bound), we look up the z-score that corresponds to a cumulative probability of 0.975. This z-score is also approximately 1.96.

z = 1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (1.96 x 8) = 48 + 15.68 = 63.68

d. Ninety-five percent of the watches refer to the range between the 2.5th and 97.5th percentiles. We already calculated the z-scores corresponding to these percentiles in part c: -1.96 and 1.96.

To find the range in months,

we convert the z-scores back:

\(x_{1}\)= μ +\(z_{1}\) x σ = 48 + (-1.96) x 8 = 32.32 months,

and \(x_{2}\)= μ + \(z_{2}\) x σ

= 48 + 1.96 x 8

= 63.68 months.

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Answer:

A

Step-by-step explanation:

In pattern A, we see that each number is 3 more than the one before it. B is incorrect because the pattern is +9. C is incorrect because the numbers in Pattern A is 3x Less than the corresponding numbers in Pattern B. D is incorrect because the numbers in Pattern B are 3x more than the numbers in Pattern A.

Hope this helps!

Answer:

Yes I agree with the person above because pattern A is adding by 3.

Answer: A

Step-by-step explanation: you start at -4 the up over 4

Answer:$1,942.50

Step-by-step explanation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 2.5%/100 = 0.025 per year.

Solving our equation:

A = 1850(1 + (0.025 × 2)) = 1942.5

A = $1,942.50

The total amount accrued, principal plus interest, from simple interest on a principal of $1,850.00 at a rate of 2.5% per year for 2 years is $1,942.50.

Answer:

C, I got it right

Step-by-step explanation:

The two major types of series are the arithmetic series and the geometric series. The arithmetic series is characterized by common difference, while the geometric series has common ratio between two successive terms.

The sum of the given series is:

\(\lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )\)

The given series is a geometric series. So, we first calculate the common ratio (r) using:

\(r = T_2 \div T_1\)

From the series, we have:

\(T_1 = \frac{1}{4}\)

\(T_2 = \frac{1}{16}\)

So, the equation becomes

\(r = \frac{1}{16} \div \frac{1}{4}\)

Rewrite as product

\(r = \frac{1}{16} * \frac{4}{1}\)

\(r = \frac{1}{4}\)

The formula to calculate the sum of a geometric series of is:

\(S_n = \frac{a(1 - r^n )}{1-r}\)

Where

\(a = T_1 =\frac{1}{4}\) -- the first term

\(S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{1-\frac{1}{4}}\)

Simplify the denominator

\(S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{\frac{3}{4}}\)

Divide 1/4 by 3/4

\(S_n = \frac{1}{3}(1 - \frac{1}{4}^n )\)

We can conclude that, the sum of the series is:

\(S_n = \lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )\)

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1) ABCD is a parallelogram (given)

2) \(\overline{BC} \parallel \overline{AD}, \overline{AB} \parallel \overline{CD}\) (opposite sides of a parallelogram are parallel)

3) \(\angle BCA \cong \angle CAD, \angle BAC \cong \angle ACD\) (alternate interior angles theorem)

4) \(\angle A \cong \angle C, \angle B \cong \angle D\) (congruent angles added to congruent angles form congruent angles)

Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

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The direction cosines of a vector are the cosines of the angles between the vector and the three mutually perpendicular axes of a coordinate system.

The direction cosines of a vector \($\mathbf{a}$\) are denoted by l, m and n. Mathematically, the relation between these direction cosines is given by:

\($$\mathbf{a}=l\mathbf{\hat{i}}+m\mathbf{\hat{j}}+n\mathbf{\hat{k}}$$\)

where i,j and k  are unit vectors along the three axes of the coordinate system.

To calculate the direction cosines of a given vector \($\mathbf{a}$\) with components \($a_x$, $a_y$ and $a_z$\), we can use the following formula:

\($$l = \frac{a_x}{\sqrt{a_x^2+a_y^2+a_z^2}}$$\)

\($$m = \frac{a_y}{\sqrt{a_x^2+a_y^2+a_z^2}}$$ \\ $$n = \frac{a_z}{\sqrt{a_x^2+a_y^2+a_z^2}}$$\)

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Answer:

volume is L × W x

Step-by-step explanation:

15 x 12 x 6

see attached I wrote down for you.

Answer:

360 ft³

Step-by-step explanation:

Volume of a rectangular pyramid = (lwh)/3 = (12x6x15) / 3 = 1080/3 = 360 ft³

V = (length x width x height) ÷ 3

In order to prove that the product of the slopes of lines AC and BC is -1, the blanks should be completed with these;

"The slope of AC or GC is \(\frac{GF}{FC}\) by definition of slope. The slope of BC or CE is \(\frac{DE}{CD}\) by definition of slope."

"∠FCD = ∠FCG + ∠GCE + ∠ECD by angle addition postulate. ∠FCD = 180° by the definition of a straight angle, and ∠GCE = 90° by definition of perpendicular lines. So by substitution property of equality 180° = ∠FCG + 90° + ∠ECD. Therefore 90° - ∠FCG = ∠ECD, by subtraction property of equality. We also know that 180° = ∠FCG + 90° + ∠CGF by the triangle sum theorem and by the subtraction property of equality 90° - ∠FCG = ∠CGF, therefore ∠ECD = ∠CGF by the substitution property of equality. Then, ∠ECD ≈ ∠CGF by the definition of congruent angles. ∠GFC ≈ ∠CDE because all right angles are congruent. So by AA, ∆GFC ~ ∆CDE. Since the ratio of corresponding sides of similar triangles are proportional, then \(\frac{GF}{CD}=\frac{FC}{DE}\) or GF•DE = CD•FC by cross product. Finally, by the division property of equality \(\frac{GF}{FC}=\frac{CD}{DE}\). We can multiply both sides by the slope of line BC using the multiplication property of equality to get \(\frac{GF}{FC}\times -\frac{DE}{CD}=\frac{CD}{DE} \times -\frac{DE}{CD}\). Simplify so that \(\frac{GF}{FC}\times -\frac{DE}{CD}= -1\) . This shows that the product of the slopes of AC and BC is -1."

In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1 × m₂ = -1

m₂ = -1

In this context, we can prove that the product of the slopes of perpendicular lines AC and BC is equal to -1 based on the following statements and reasons;

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Answer:

point form:(13/5, -3/5)

equation form: x=13/5

                         y=-3/5

Step-by-step explanation:

Give me brianliest, appreciated. Peace✌

Answer:

900 ml of milk

Step-by-step explanation:

the scale is 1:1 so just multiply by 3

The required equation function j which is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  \(j(x)= (x+2)^{1/2}\)  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

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In the question the graph is missing, a graph has been added on behalf of the incomplete question.

Answer:

3rd one

4th one

5th one

8th one

Step-by-step explanation:

solve for the y intercept by plugging in f(0)

0²-4(0)-21= -21

Therefore (0,-21) is a y intercept

Factor to find the x intercepts

(x+3)(x-7)

Therefore the intercepts are

(-3,0) (7,0)

THis function has a positive coeficcent and an even degree

therefore as x approaches infinity it's infinity

and as x approaches negative infinity it's infinity

f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

Given that the function g(x) is a transformation of the parent function f(x).

To Decide how f(x) was transformed to make g(x).

The reflection of the point (x,y) across the line y = 1/2 x is the point (y, x).

By the given tables we can see that;

g(x) = 1/2 f (x)

Therefore, f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.

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The value of tan(t−π) is 4/9.

According to the statement

we have given that  tan(t)=4/9 and we have to find the value of tan(t−π).

So,

tan(t−π)  -(1)

take negative sign common from equation (1) it then

tan(t−π) = -tan(-t+π)

and we know that the according to the mathematics formula it become

tan(-t+π) is -tan t

then

tan(t−π) = -(-tan t)

it becomes

tan(t−π) = tan t

then its value becomes

tan(t−π) = tan(t)=4/9.

because we have given that the value of tan t is tan(t)=4/9.

So, The value of tan(t−π) is 4/9.

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Answer:

. The actual mass of the object was 9.98 X 10-3 g.

Step-by-step explanation:

yeah

To write out the joint probability for the given sentence using the chain rule, we can express it as follows: p(There, is, only, one, person, who, is, not, ordinary) =

p(There) * p(is | There) * p(only | is, There) * p(one | only, is, There) *, p(person | one, only, is, There) * p(who | person, one, only, is, There) *,p(is | who, person, one, only, is, There) * p(not | is, who, person, one, only, is, There) *,p(ordinary | not, is, who, person, one, only, is, There).

This expression applies the chain rule to break down the joint probability of the sentence into the product of the conditional probabilities of each word given the preceding words in the sentence. To write out the probability using the second-order Markov assumption, we assume that the probability of each word only depends on the two preceding words. Therefore, we can express the probability as follows:

p(There, is, only, one, person, who, is, not, ordinary) = p(There) * p(is | There) * p(only | There, is) * p(one | is, only) *
p(person | only, one) * p(who | one, person) * p(is | person, who) *
p(not | who, is) * p(ordinary | is, not)
This expression only considers the two preceding words for each word in the sentence, which is the second-order Markov assumption.

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