Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability 0.23 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent. Give your answer to four decimal places. a. What is the probability that both professors get their grants funded

Answer:

x < 5 or x > 1

Step-by-step explanation:

2x - 6 < 4

2x < 4 + 6

2x < 10

x < 10/2

x < 5

2x - 6 > - 4

2x > - 4 + 6

2x > 2

x > 2/2

x > 1

Answer:

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Step-by-step explanation:

Explanation:-

Given data Z = -2 and Z =2

The probability that

P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)

                   = 0.5 + A(2) - ( 0.5 - A(-2))

                  = A (2) + A(-2)

                 = 2 × A(2)     (∵ A(-2) = A(2)

                = 2×0.4772

              = 0.9544

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Answer:

  (x, y) ⇒ (2x, y)

Step-by-step explanation:

Any rigid transformation or dilation will be a similarity transformation. A transformation that doesn't preserve similarity will be none of those, so may be non-linear or different in one direction than another.

Several possibilities come to mind:

  (x, y) ⇒ (2x, y) . . . . . . stretches x, but not y

  (x, y) ⇒ (x+y, y) . . . . . a "shear" transformation

  (x, y) ⇒ (x, y^(3/2)) . . . . . a non-linear transformation

These only transform one coordinate. Of course, different transforms or combinations can be used on the different coordinates.

__

The attachment shows the effect of each of these. The red figure is the original icosagon (20-gon). The blue figure shows the horizontal stretch of the first transformation. The green figure shows the diagonal stretch of the shear transformation. The purple figure shows the effect of a non-linear transformation.

Answer:

x = 3 or x = -5

Step-by-step explanation:

x² + 2x - 15 = 0

Factor left side of equation.

(x - 3)(x + 5) = 0

Set factors equal to 0

x - 3 = 0

x = 3

x + 5 = 0

x = -5

Answer:

-9≤y≤8

Step-by-step explanation:

The range is the output values

Y goes from -9 to 8

-9≤y≤8

Answer:

-9≤y≤8

Step-by-step explanation:

That is the correct answer on plato.

Answer:

The probability of the plants being tall is equal to P(TT) + P(Tt)= 1/4+1/2=3/4

Step-by-step explanation:

Hello!

The characteristic "height" of a plant is determined by the alleles "tall" T (dominant) and "short" a (recessive). If both parents are Tt, you have to calculate the probability of the offspring being tall (TT or Tt)

To construct the Punnet square you have to make a table, where the parental alleles will be in the margins, for example: the father's alleles in the columns and the mother's alleles in the rows.

Each parent will produce a haploid gamete that will carry one of the alleles, so the probability for the offspring receiving one of the alleles is 1/2

Father (Tt): gametes will carry either the dominant allele T or the recessive allele t with equal probability 1/2

Mother (Tt): gametes will also carry either the dominant allele T or the recessive allele t with equal probability 1/2

Then you have to cross each allele to determine all possible outcomes for the offsprings. For each cell, the probability of obtaining both alleles will be the product of the probability of each allele (See attachment)

First combination, the offspring will receive one dominant allele from his father and one dominant allele from his mother: TT, the probability of obtaining an offspring with this genotype will be P(T) * P(T) = 1/2*1/2=1/4

Second combination, the offspring will receive the recessive allele from the father and the dominant allele from the mother, then its genotype till be tT with probability: P(t)*P(T)= 1/2*1/2=1/4

Third combination, the offspring will receive one dominant allele from his father and one recessive allele from his mother, the resulting genotype will be Tt with probability: P(T)*P(t)= 1/2*1/2=1/4

Combination, the offspring will receive both recessive alleles from his parents, the resulting genotype will be tt with probability: P(t)*P(t)= 1/2*1/2=1/4

So there are three possible genotypes for the next generation:

TT with probability P(TT)= 1/4

Tt with probability: P(Tt)+P(tT)=1/4+1/4=1/2⇒ This genotype is observed twice so you have to add them.

tt with probability P(tt)= 1/4

Assuming this genotype shows complete dominance, you'll observe the characteristic "Tall" in individuals that carry the dominant allele "T", i.e. individuals with genotype "TT" and "Tt"

So the probability of the plants being tall is equal to P(TT) + P(Tt)= 1/4+1/2=3/4

I hope this helps!

Answer:

(6, 3)

Step-by-step explanation:

x=6 y=3

2(6) -3 =9

12 -3 = 9

Answer:

(3,-3)

but there are infinately many more.

Step-by-step explanation:

We need to find a pair of numbers that when substituted in 2x-y we get 9.

because this equation is linear there are actually an infinite number of solutions. So all we have to to is pick a random number for x, say 3, and there will only be 1 value of y that will satisfy the equation, so we just plug it in.

let x =3

2x - y = 9 ⇒ 2×3 - y = 9

                ⇒ 6 -y = 9

                ⇒ -y = 3

                ⇒ y = -3

so (3,-3) is a solution

Answer:

Si el cuadrado de la mitad del número de horas que faltan transcurrir del día coinciden con el número de horas transcurridas del día, son las 16:00 hs.

Step-by-step explanation:

Si el cuadrado de la mitad del número de horas que faltan transcurrir del día coinciden con el número de horas transcurridas del día, son las 16:00 hs.

Esto es así porque, como primera medida, la mitad de horas que faltan transcurrir del día no puede ser mayor a 4, puesto que 5 al cuadrado da como resultado 25, es decir, excede el número de horas que tiene un día.

Entonces, siguiendo con dicho razonamiento en sentido decreciente, tenemos que 4 al cuadrado da como resultado 16 (4 x 4). En este caso, 4 sería la mitad de horas que faltan transcurrir en el día, y 16 las horas ya transcurridas. Entonces, como 16 mas 8 da 24, y esa es la cantidad de horas que tiene el día, ésta es la opción correcta.

Answer:

351.5

Step-by-step explanation:

Step 1: Convert fractions to improper

(2.8(14/5(8.75 - 5/2)))7.25 - 15/4

Step 2: Parenthesis

(2.8(14/5(6.25)))7.25 - 15/4

Step 3: Parenthesis

(2.8(17.5))7.25 - 15/4

Step 4: Parenthesis

49(7.25) - 15/4

Step 5: Multiply

355.25 - 15/4

Step 6: Subtract

351.5

Answer:

5n + 10

Step-by-step explanation:

We would like to find the sum of these 5 integers. Simply add them up:

n + (n + 1) + (n + 2) + (n + 3) + (n + 4) = 5n + (1 + 2 + 3 + 4) = 5n + 10

The answer is thus 5n + 10.

~ an aesthetics lover

Answer:

5n + 10

Step-by-step explanation:

We need to add the five consecutive integers.

n + n + 1 + n + 2 + n + 3 + n + 4

Rearrange.

n + n + n + n + n + 1 + 2 + 3 + 4

Add.

5n + 10

Answer:

36°

Step-by-step explanation:

[tex]size \: of \: one \: exterior \: angle \\ \\ = \frac{360 \degree}{no \: of \: sides} \\ \\ = \frac{360 \degree}{10} \\ \\ = 36 \degree[/tex]

Answer:

Exterior Angle = 36 degrees

Step-by-step explanation:

The measure of each interior angle of the decagon is 144

So,

Exterior Angle = 180 - 144    (Interior and Exterior angles are angles on a straight line hence adding up to 180 degrees)

Exterior Angle = 36 degrees

Answer:

  9 and 18

Step-by-step explanation:

The numbers are in the ratio 1 : 2, so the ratio of the smaller to the total is ...

  1 : (1+2) = 1 : 3

1/3 of 27 is 9, the value of the smaller number. The larger number is double this, so is 18.

The numbers are 9 and 18.

Answer:

9 and 18

Step-by-step explanation:

you know the explanation since another guy put it

Answer:

The price of taco should be $6

Step-by-step explanation:

The rule is that the price of a food item should be four times the price of the ingredients used in making the food item.

mathematically,

[tex]y = 4x[/tex]

where [tex]y[/tex] is the price of the food item

[tex]x[/tex] is the price of the ingredients

If the price of ingredients for making taco is 1.5 dollars

price of taco = ?

substituting into the equation

[tex]y[/tex] = 4(1.5) = $6

Question Correction

One common system for computing a grade point average​ (GPA) assigns 4 points to an​ A, 3 points to a​ B, 2 points to a​ C, 1 point to a​ D, and 0 points to an F. What is the GPA of a student who gets an A in a 3​-credit ​course, a B in each of three 4​-credit ​courses, a C in a 2​-credit ​course, and a D in a 3​-credit ​course?

Answer:

2.75

Step-by-step explanation:

We present the information in the table below.

[tex]\left|\begin{array}{c|c|c|c}$Course Grade&$Grade Point(x)&$Course Credit(y)&$Product(xy)\\---&---&---&---\\A&4&3&12\\B&3&4&12\\B&3&4&12\\B&3&4&12\\C&2&2&4\\D&1&3&3\\---&---&---&---\\$Total&&20&55\end{array}\right|[/tex]

Therefore, the GPA of the student is:

[tex]GPA=\dfrac{55}{20}\\\\ =2.75[/tex]

Answer:

  7.2 volts

Step-by-step explanation:

3% of 240 is ...

  0.03 × 240 = 3 × 2.40 = 7.20

The maximum allowable drop on a 240-volt circuit is 7.2 volts.

Answer:

7

Step-by-step explanation:

This a special 90° 45° 45° triangle and is an Isosceles triangle at the same time

Of one of the equal side is 7 than the other one too must be 7

Answer:

7

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Two secants drawn to a circle from an external point, then

The product of the measures of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.

Thus

x × 12 = 4 × 9

12x = 36 ( divide both sides by 12 )

x = 3

Answer:

a) The length of the building that should border the dog run to give the maximum area = 25feet

b)    The maximum area of the dog run  = 1250 s q feet²

Step-by-step explanation:

Step(i):-

Given function

                       A(x) = x (100-2x)

                      A (x) = 100x - 2x²...(i)

Differentiating equation (i) with respective to 'x'

             [tex]\frac{dA}{dx} = 100 (1) - 2 (2x)[/tex]

     ⇒    [tex]\frac{dA}{dx} = 100 - 4 x[/tex]      ...(ii)

Equating  zero

         ⇒ 100 - 4x =0

         ⇒  100 = 4x

Dividing '4' on both sides , we get

             x = 25

Step(ii):-

Again differentiating equation (ii) with respective to 'x' , we get

    [tex]\frac{d^{2} A}{dx^{2} } = -4 (1) < 0[/tex]

Therefore The maximum value at x = 25

The length of the building that should border the dog run to give the maximum area = 25

Step(iii)

  Given  A (x) = x ( 100 -2 x)

substitute  'x' = 25 feet

             A(x) = 25 ( 100 - 2(25))

                    = 25(50)

                   = 1250

Conclusion:-

   The maximum area of the dog run  = 12 50  s q feet²

Answer: z < 36

Step-by-step explanation: To solve for z in this inequality, we multiply by 12 on both sides of the inequality to get z < 36.

We can write this in set notation as {z: z < 36}.

━━━━━━━☆☆━━━━━━━

▹ Answer

z < 36

▹ Step-by-Step Explanation

[tex]\frac{z}{12} < 3\\\\12 * \frac{z}{12} < 12 * 3\\\\z < 12 * 3\\\\z < 36[/tex]

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)

Step-by-step explanation:

Given the line

[tex]y = 2x- 7[/tex]

Given the missing coordinates:

(4.75, )

(, –7.7)

(0.4, )

We know that every coordinate is of the form [tex](x,y)[/tex].

So, we can easily solve the for other variable if one variable is given from the given line using the graph or the given equation.

For the first coordinate:

(4.75, )

From graph it can be found that y = 2.5

Verifying using the equation.

Putting the value of x = 4.75 in the equation we get:

y = 2[tex]\times[/tex] 4.75 - 7

y = 9.5 - 7 = 2.5

So, the coordinate is  (4.75, 2.5)

For the second coordinate:

(, -7.7 )

From graph it can be found that x = -0.35

Verifying using the equation:

Putting the value of y = -7.7 in the equation we get:

-7.7 = 2x - 7

2x = -7.7 + 7 = -0.7

x = -0.35

So, the coordinate is  (-0.35, -7.7).

For the third coordinate:

(0.4, )

From graph it can be found that y = -6.2

Verifying using the equation.

Putting the value of x = 0.4 in the equation we get:

y = 2[tex]\times[/tex] 0.4 - 7

y = 0.8 - 7 = -6.2

So, the coordinate is  (0.4, -6.2)

Also, please refer to the attached graph.

So, the answer is:

(4.75, 2.5), (-0.35, -7.7), (0.4, -6.2)

Answer: its 2.5, -0.35, -6.2

Step-by-step explanation: in easier words

Answer:

2/3

Step-by-step explanation:

There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.

Answer:

Step-by-step explanation:

This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.

Answer:

by using distance formula

d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

by putting the values of coordinates

[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]

[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]

[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]

[tex]d=\sqrt{6.25+100}[/tex]

[tex]d=\sqrt{106.25}[/tex]

[tex]d=10.3[/tex]

Step-by-step explanation:

i hope this will help you :)

Split up the interval [0, 3] into 6 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]

The right endpoints are given by the arithmetic sequence,

[tex]r_i=0+\dfrac i2=\dfrac i2[/tex]

with [tex]1\le i\le6[/tex].

We approximate the integral of [tex]f(x)[/tex] on the interval [0, 3] by the Riemann sum,

[tex]\displaystyle\int_0^3f(x)\,\mathrm dx=\sum_{i=1}^6f(r_i)\Delta x_i[/tex]

[tex]\displaystyle=\frac{3-0}6\sum_{i=1}^6\left(3{r_i}^2-8r_i\right)[/tex]

[tex]\displaystyle=\frac12\sum_{i=1}^6\left(\frac{3i^2}4-4i\right)[/tex]

[tex]\displaystyle=\frac38\sum_{i=1}^6i^2-2\sum_{i=1}^6i[/tex]

Recall the formulas,

[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]

[tex]\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6[/tex]

Then the value of the integral is approximately

[tex]\displaystyle=\frac38\cdot\frac{6\cdot7\cdot13}6-2\cdot\frac{6\cdot7}2=\boxed{-\frac{63}8}=-7.875[/tex]

Compare to the exact value of the integral, -9.

The Riemann sum of [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex] with [tex]n = 6[/tex] is [tex]-\frac{63}{8}[/tex].

The formula for the right Riemann sum is described below:

[tex]S = \frac{b-a}{n} \cdot \Sigma\limit_{i= 1}^{n} \,f(x+i\cdot \frac{b-a}{n} )[/tex] (1)

Where:

If we know that [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex], [tex]a = 0[/tex], [tex]b = 3[/tex] and [tex]n = 6[/tex], then the Riemann sum is:

[tex]S = \frac{3-0}{6}\cdot [f(0.5) + f(1) + f(1.5) + f(2) + f(2.5) +f(3)][/tex]

[tex]S = \frac{1}{2}\cdot \left(-\frac{13}{4}-5-\frac{21}{4}-4-\frac{5}{4}+3\right)[/tex]

[tex]S = -\frac{63}{8}[/tex]

The Riemann sum of [tex]f(x) = 3\cdot x^{2}-8\cdot x[/tex] with [tex]n = 6[/tex] is [tex]-\frac{63}{8}[/tex].

We kindly invite to check this question on Riemann sum: https://brainly.com/question/23960718

Answer:

R= diameter ÷ 2

Step-by-step explanation:

the radius is half the diameter.

Answer:

There is a 95% confidence that the sample has a mean between 158.92 pounds and 171.48 pounds

Step-by-step explanation:

Given that mean (μ) = 165.2 pounds, standard deviation (σ) = 12.4 pounds, sample size (n) = 15 crates. Confidence (C) = 95% = 0.95

α = 1 - C = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

The z score of α/2 corresponds to the z score of 0.475 (0.5 - 0.025) which is 1.96. [tex]z_{\frac{\alpha}{2} }=1.96[/tex]

The margin of error (E) is given by:

[tex]E=z_{\frac{\alpha}{2} }\frac{\sigma}{\sqrt{n} } =1.96*\frac{12.4}{\sqrt{15} }= 6.28[/tex]

The confidence interval = μ ± E = 165.2 ± 6.28 = (158.92, 171.48)

The confidence interval is between 158.92 pounds and 171.48 pounds. There is a 95% confidence that the sample has a mean between 158.92 pounds and 171.48 pounds

Answer:

4

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf xy-5x+4y-20}[/tex]

Step-by-step explanation:

[tex]\sf (x+4)(y-5)\\\\Resolving \ Parenthesis\\\\= x(y-5)+4(y-5)\\\\= xy-5x+4y-20\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

a) Mean of X = 0.40

Variance of X = 0.24

b) Y is a Bernoulli's distribution. Check Explanation for reasons.

c) Mean of Y = 0.80 points

Variance of Y = 0.96

Step-by-step explanation:

a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.

Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.

The probability mass function of X is then

X | Probability of X

0 | 0.60

1 | 0.40

The mean is given in terms of the expected value, which is expressed as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40

Variance = Var(X) = Σx²p − μ²

μ = mean = E(X) = 0.40

Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40

Variance = Var(X) = 0.40 - 0.40² = 0.24

b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.

A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).

Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.

The probability mass function for Y is then

Y | Probability of Y

0 | 0.60

2 | 0.40

c) Mean and Variance of Y

Mean = E(Y)

E(Y) = Σ yᵢpᵢ

yᵢ = each variable

pᵢ = probability of each variable

E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points

Variance = Var(Y) = Σy²p − μ²

μ = mean = E(Y) = 0.80

Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60

Variance = Var(Y) = 1.60 - 0.80² = 0.96

Hope this Helps!!!

Answer:

11.70% probability that the mean height for the sample is greater than 64 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 63.5, \sigma = 2.96, n = 50, s = \frac{2.96}{\sqrt{50}} = 0.4186[/tex]

What is the probability that the mean height for the sample is greater than 64 inches?

This is 1 subtracted by the pvalue of Z when X = 64.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{64 - 63.5}{0.4186}[/tex]

[tex]Z = 1.19[/tex]

[tex]Z = 1.19[/tex] has a pvalue of 0.8830

1 - 0.8830 = 0.1170

11.70% probability that the mean height for the sample is greater than 64 inches

Answer:

look up the basic rules for sin and cos

Step-by-step explanation: