Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. ASAPostulate

Answer:

Angle b is congruent to angle E

CA=FD

Step-by-step explanation:

If _______, then triangle ABC and triangle DEF are congruent by the ASA criterion.  ASA is angle side angle .  We know angle C= angle F and side CB = side FE We need to know angle B = angle E

If _______, then triangle ABC and triangle DEF are congruent by the SAS criterion.  SAS is side angle side,  we know side CB = side FE  and then angle C= angle F then we need side CA = side FD

If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.

If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.

Two figures are said to be congruent of they have the same shape and all the corresponding sides and angles are congruent.

The HL (hypotenuse leg) congruence theorem states that if the hypotenuse and one leg of a triangle is congruent to another triangle, then both triangles are congruent.

In triangle ABC and DEF;

BC = EF and ∠ACB ≅ ∠DFE

Hence:

If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.

If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.

Find out more on congruent figures at: https://brainly.com/question/1675117

Answer:

12.56 cents

14.08 cent

Step-by-step explanation:

The unit price for each of the following items could be obtained thus :

The unit price = price of one item

Therefore, given that x numbers of a certain item cost y ;

The unit price will be : y / x

frozen orange juice

16.0 oz at $2.01

12 oz at $1.69

If 16 oz cost $2.01

1 oz = $2.01 / 16 = $0.125625 * 100 = 12.56 cents

If 12 oz = $1.69

1 oz = $1.69 / 12 = $0.1408333 * 100 = 14.08 cent

Answer: D

Step-by-step explanation:

(lines parallel to each other have the same slope)

slope = m = 2

y = mx + b, (5,6)

6 = 2(5) + b

6 = 10 + b

b = -4

y = 2x - 4

y - 6 = 2(x - 5)

y - 6 = 2x - 10

y = 2x -4

Answer:

Check the photo for the answer

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

;)

Answer:

No

Step-by-step explanation: Bye

Answer:

D. 157

Step-by-step explanation:

4(x^2+3)-2y

4(6^2+3)-2(-1/2) add in given values

4(39)+1.     start with parentheses

156+1.        combine like terms

157.            answer

Answer:

D. 157

Step-by-step explanation:

Hi there!

We want to find the value of the expression 4(x²+3)-2y is when x=-6 and y=-1/2

Let's first simplify the expression, as that will likely make it easier

Distribute 4 to both x² and 3

4x²+12-2y

That's the expression

Substitute -6 as x into the expression

4(-6)²+12-2y

Raise (-6) to the second power

4*36+12-2y

Multiply 36 by 4

144+12-2y

Add 12 and 144 together

156-2y

Now the expression is 156-2y

But remember that we know that y=-1/2, and we haven't substituted it into the expression yet

Substitute -1/2  as y into the expression

156-2(-1/2)

Multiply

156+2/2

Simplify

156+1

Add

157

Hope this helps!

Answer:

Step-by-step explanation:

a) 0.5*0.365=18.25%

b) (100%-20,7%-50%)=29.3

Answer:

880 ft.

Step-by-step explanation:

First! We have to establish how many feet the car travels per hour.

60 (number of miles per hour) x 5280 (number of feet in a mile) = 316,800 (number of feet in an hour)

Next, since we know that there are 60 minutes in an hour we are going to divide our "number of feet in an hour" by 60 to get the "number of feet in a minute"

316,800 ÷ 60 = 5280

Once again, we are going to divide our "number of feet in a minute" by 60 to get the "number of feet per second".

5280 ÷ 60 = 88

Finally! We will multiple our "number of feet per second" by 10 to get how many feet the car can travel in 10 seconds.

88 × 10 = 880

So! Our car can travel 880 feet in 10 seconds.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

what is the time given ???

Step-by-step explanation:

either initial velocity is 0 or final velocity is zero

V=U+AT

converting it we get

V/T = u+a

V/T - U= a

where

v= final velocity

u= initial velocity

a= acceleration

t= time

plz write the full question

This question is solved using the conditional probability concept.

Using this concept, we find that:

First, the concept is presented.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]

In which

P(A|B) is the probability of event A happening, given that B happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(B) is the probability of B happening.

----------------------------------------------------

Question a:

For relation with the formula presented above, I will change events A and B.

Event A: Person is infected.

Event B: Positive test.

Probability of a positive test:

Thus:

[tex]P(B) = 0.85\frac{1}{300} + 0.05\frac{299}{300} = \frac{0.85\times1 + 0.05\times299}{300} = 0.0527[/tex]

Probability of a positive test and the person is infected.

85% = 0.85 out of 1/300. Thus:

[tex]P(A \cap B) = \frac{0.85}{300} = 0.0028[/tex]

Desired probability:

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.0028}{0.0527} = 0.053[/tex]

0.053*100% = 5.3%, thus:

P(AIB)= 5.3%

---------------------

Question b:

Event A: Does not have the virus

Event B: Test negative.

Probability of a negative test:

Thus:

[tex]P(B) = 0.15\frac{1}{300} + 0.95\frac{299}{300} = \frac{0.15\times1 + 0.95\times299}{300} = 0.9473[/tex]

Probability of a negative test and the person is not infected.

0.95 out of 299/300

Thus:

[tex]P(A \cap B) = \frac{0.95\times299}{300} = 0.9468[/tex]

Desired probability:

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.9468}{0.9473} = 0.999[/tex]

0.999*100% = 99.9%, so:

P(A'|B') = 99.9%

A similar question can be found at https://brainly.com/question/24275491

Answer:

34.55

Step-by-step explanation:

S = 34.55 represents the standard deviation of the residuals which is the correct answer that would be option (B).

A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.

Students' proficiency in math and English is assessed by a particular standardized test. Ten students were chosen at random, and their math and English test results were recorded and examined.

The computer output displays the outcomes.

Predictor    Coef     SE Coef     t-ratio        p

Constant   -124.13     78.712      0.046

Math           1.223      0.1966      6.220  0.000

S = 34.55     R-Sq = 82.8%      R-Sq (Adj) = 83.5%

In the above ANOVA table, S = 34.55 represents the residual standard deviation.

Therefore, the correct answer is Option B = 34.55.

Option A = 1.223 represents the coefficient of the math score.

Option C = 78.712 represents the Standard Error (S.E).

Option D = 124.13 is the coefficient value.

Hence, the correct answer would be an option (B).

Learn more about the standard deviation here:

https://brainly.com/question/16555520

#SPJ2

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.

tan(61) = 47 / BC

BC = 47 / tan(61)

BC = 26.05 units

Hope this helps!

Answer:

BC = 26.05

Step-by-step explanation:

SOH CAH TOA

tan 61 = 47/BC

BC = 47/tan 61

Answer: oranges 1.2 Kg and apples 0.75 Kg.

Step-by-step explanation:

Oranges (4)(1.5)/5

Apples (3)(2)/8

Answer:

A. Combination.

B. 17020

Step-by-step explanation:

A. Determination whether it is permutation or combination.

From the question given above, we were told that the student body of 185 students wants to elect two (2) representatives.

This is clearly combination because it involves a selecting process (i.e selecting 2 out of 185).

NOTE: Combination involves selecting while permutation involves arranging.

B. Determination of the combination.

Total number of people (n) = 185

Number of chosen people (r) = 2

Number of combination (ₙCᵣ) =?

ₙCᵣ = n! / (n – r)! r !

₁₈₅C₂ = 185! / (185 – 2)! 2!

₁₈₅C₂ = 185! / 183! 2!

₁₈₅C₂ = 185 × 184 × 183! / 183! 2!

₁₈₅C₂ = 185 × 184 / 2!

₁₈₅C₂ = 185 × 184 / 2 × 1

₁₈₅C₂ = 34040 / 2

₁₈₅C₂ = 17020

Answer:

A) 128

B) 7800

Step-by-step explanation:

Trial and error until I got to 75 x 104 and 60 x 128 (which abides by the fact that there has to be 24 more red boxes) which equals 7800 and 7680 and if you take them away from each other you get 120

Answer:

The probability of getting two numbers whose sum is 10 is 25%.

Step-by-step explanation:

Given that a single die is rolled twice, and there are 36 equally-likely outcomes, to find the probability of getting two numbers whose sum is 10 the following calculation must be performed:

1 = +9

2 = +8

3 = +7

4 = +6

5 = +5

6 = +4

7 = +3

8 = +2

9 = +1

9/36 = 0.25

Therefore, the probability of getting two numbers whose sum is 10 is 25%.

Answer: [tex]y=-\frac{2}{5}x+12[/tex]

y = mx + b

m = slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{18-8}{-15-10}=\frac{10}{-25}=\frac{2(5)}{-5(5)}=-\frac{2}{5}[/tex]

The y-intercept(b) can be found by substituting a point into the function.

[tex]y = -\frac{2}{5}x + b \\\\8=-\frac{2}{5}(10) + b\\\\8=-4+b\\\\b=8+4=12[/tex]

Therefore, the function is:

[tex]y=-\frac{2}{5}x+12[/tex]

Answer:

Perimeter

[tex]202 = x + x + 26 + 4x + 26 + 4x\\202-26-26=10x\\150=10x\\x=15[/tex]

Therefore, the dimensions are

Answer:

Ray weighed 150 pounds two years ago.

Step-by-step explanation:

11/100 = 16.5/x

11x = 16.5(100)

11x = 1,650

(11x)/11 = (1,650)/11

x = 150

About time that he should start going to the gym!

Solution :

Let [tex]p_1[/tex] and [tex]p_2[/tex]  represents the proportions of the seeds which germinate among the seeds planted in the soil containing [tex]3\%[/tex] and [tex]5\%[/tex] mushroom compost by weight respectively.

To test the null hypothesis [tex]H_0: p_1=p_2[/tex] against the alternate hypothesis  [tex]H_1:p_1 \neq p_2[/tex] .

Let [tex]\hat p_1, \hat p_2[/tex] denotes the respective sample proportions and the [tex]n_1, n_2[/tex] represents the sample size respectively.

[tex]$\hat p_1 = \frac{74}{155} = 0.477419[/tex]

[tex]n_1=155[/tex]

[tex]$p_2=\frac{86}{155}=0.554839[/tex]

[tex]n_2=155[/tex]

The test statistic can be written as :

[tex]$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}[/tex]

which under [tex]H_0[/tex]  follows the standard normal distribution.

We reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance, if the P-value [tex]<0.05[/tex] or if [tex]|z_{obs}|>Z_{0.025}[/tex]

Now, the value of the test statistics = -1.368928

The critical value = [tex]\pm 1.959964[/tex]

P-value = [tex]$P(|z|> z_{obs})= 2 \times P(z< -1.367928)$[/tex]

                                     [tex]$=2 \times 0.085667$[/tex]

                                     = 0.171335

Since the p-value > 0.05 and [tex]$|z_{obs}| \ngtr z_{critical} = 1.959964$[/tex], so we fail to reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance.

Hence we conclude that the two population proportion are not significantly different.

Conclusion :

There is not sufficient evidence to conclude that the [tex]\text{proportion}[/tex] of the seeds that [tex]\text{germinate differs}[/tex] with the percent of the [tex]\text{mushroom compost}[/tex] in the soil.

Answer:

32.64°

Step-by-step explanation:

From triangle Given :

The sides of the missing angle given are the Adjacent and hypotenus.

Since the triangle is right angled, we can apply trigonometry :

cosθ = adjacent / hypotenus

Cosθ = 16 / 19

θ = Cos^-1(16/19)

θ = 32.6368

θ = 32.64°

Answer:

If you multiply a decimal by 10, the decimal point will move one place to the right. If you divide a decimal by 10, the decimal point will move one place to the left.

Step-by-step explanation:

Multiplying a decimal by 10 increases the value of each digit by 10. Multiplying a decimal by a power of 10 increases the value of each digit by a number of times that is equivalent to that power of 10. When a digit's value is changed, that digit is moved to the appropriate place.

Answer:

D

Step-by-step explanation:

Assuming that the expression is referring to sin²(2πft) and not sin²(2)πft, we can solve as follows:

One trigonometric identity states that sin²x+cos²x = 1. We want to express this in terms of cos²x, so we need to solve for sin²x. Subtracting cos²x from both sides, we get 1-cos²x = sin²x. Plugging (2πft) for x, we get

1-cos²(2πft) = sin²(2πft)

We can plug that into our equation to get

P = I₀²R(1-cos²(2πft)), or D

Answer:

a. L{t} = 1/s² b. L{1} = 1/s

Step-by-step explanation:

Here is the complete question

The The Laplace Transform of a function ft), which is defined for all t2 0, is denoted by Lf(t)) and is defined by the improper integral Lf))s)J" e-st . f(C)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of s as a fixed constant) 1. Find Lft) (hint: remember integration by parts) A. None of these. B. O C. D. 1 E. F. -s2 2. Find L(1) A. 1 B. None of these. C. 1 D.-s E. 0

Solution

a. L{t}

L{t} = ∫₀⁰⁰[tex]e^{-st}t[/tex]

Integrating by parts  ∫udv/dt = uv - ∫vdu/dt where u = t and dv/dt = [tex]e^{-st}[/tex] and v = [tex]\frac{e^{-st}}{-s}[/tex] and du/dt = dt/dt = 1

So, ∫₀⁰⁰udv/dt = uv - ∫₀⁰⁰vdu/dt w

So,  ∫₀⁰⁰[tex]e^{-st}t[/tex] =  [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ -  ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]

∫₀⁰⁰[tex]e^{-st}t[/tex] =  [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ -  ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]

= -1/s(∞exp(-∞s) - 0 × exp(-0s)) + [tex]\frac{1}{s}[/tex] [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰

= -1/s[(∞exp(-∞) - 0 × exp(0)] - 1/s²[exp(-∞s) - exp(-0s)]

= -1/s[(∞ × 0 - 0 × 1] - 1/s²[exp(-∞) - exp(-0)]

= -1/s[(0 - 0] - 1/s²[0 - 1]

= -1/s[(0] - 1/s²[- 1]

= 0 + 1/s²

= 1/s²

L{t} = 1/s²

b. L{1}

L{1} = ∫₀⁰⁰[tex]e^{-st}1[/tex]

= [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰

= -1/s[exp(-∞s) - exp(-0s)]

= -1/s[exp(-∞) - exp(-0)]

= -1/s[0 - 1]

= -1/s(-1)

= 1/s

L{1} = 1/s

Answer:5

Step-by-step explanation: root5a+2 +7a-8 = 0

 squaring both side

5a+2=7a-8

8+2=7a-5a

10=2a

a=5

Answer:

[tex]\sqrt{5a+2}-\sqrt{7a-8}=0[/tex]

Isolate a square root on the left-hand side

[tex]\sqrt{5a+2} =\sqrt{7a-}8+0[/tex]

Eliminate the radical :-

[tex]5a+2 = 7a-8[/tex]

Solve:-

[tex]2a -10 = 0[/tex]

Add  10  to both sides, then Divide both sides by 2:-

[tex]a = 5[/tex]

OAmalOHopeO

Answer:

top right

Step-by-step explanation:

roots of an equation = x-intercepts

Answer:

top right is the answer from my calculatins

Answer:

The slope is -4.

Step-by-step explanation:

Slope(m)=(y2-y1)/(x2-x1)

y2=-7, y1=-19, x2=-2, x1=1

(-7+19)/(-2-1)

=12/-3

=-4

Answer: -4

Step-by-step explanation:

The slope formula is: [tex]y_{2} -y_{1}/x_{2}-x_{1} \\[/tex]

So it is: (-7+19)/(-2-1) = 12/-3 = -4

I hope this helped!