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likoan [24]
3 years ago
11

3x+8y=27 4x+3y=13 solve the simultaneous equation

Mathematics
1 answer:
dmitriy555 [2]3 years ago
4 0

Step-by-step explanation:

3x+8y=27

3x=27-8y

x=27-8y/3

4(27-8y/3) + 3y=13

36-32/3y +3y =13

36-23/3y=13

36-13=23/3y

y=3

x=1

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How many terms are there in a geometric series if the first term is 3, the common ratio is 4 and the sum of the series is 1,023
Olenka [21]
The sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r) in our case:

s(n)=3(1-4^n)/(1-4)

s(n)=-(1-4^n)

s(n)=(4^n)-1  and s=1023

(4^n)-1=1023

4^n=1024

n ln4=ln1024

n=(ln1024)/(ln4)

n=5
4 0
3 years ago
Which is a better relative position, a score of 83 on a geography test that has a mean of
malfutka [58]

Answer:

i dont kknow

Step-by-step explanation:

5 0
2 years ago
Devise the exponential growth function that fits the given data, then answer to accompanying question. Be sure to identify the r
Free_Kalibri [48]

Answer:

In 20 years, the population will be about 80.3 thousand people

Step-by-step explanation:

If our first time is 0 and the population that goes along with that time is 70,000, we have a coordinate point where x is the time (0), and y is the population at that time (70).  Our next time is 10 years later, when the population is 75,000.  The coordinate point for that set of data is (10, 75).  Now we will use those 2 points in the standard form of an exponential equation to write the model for this particular situation.  

Exponential equations are of the form

y=a(b)^x

where x and y are the coordinates from our points, one at a time; a is the initial value, and b is the growth rate.  Filling in an equation with the first set of data:

70=a(b)^0

Anything raised to the power of 0 = 1, so b to the power of 0 = 1 and we simply have that a = 70.

Now we use that value of a along with the x and y from the next coordinate pair to solve for b:

75=70(b)^{10}

Begin by dividing both sides by 70 to get

1.071428571=b^{10}

Undo the power of 10 on the right by taking the 10th root of both sides:

(1.071428571)^{\frac{1}{10}}=(b^{10})^{\frac{1}{10}}

On the right side we simply have b now, and on the left we have

1.006923142=b

Now we have a and b to write the model for this situation:

y=70(1.006923142)^x

We need to find y, the population, in x = 20 years:

y=70(1.006923142)^{20}

Raise the parenthesis to the 20th power giving you

y = 70(1.147959784) and

y = 80.3 thousand people

7 0
3 years ago
Grant has fraction 2 over 3 of a cup of ice cream in a bowl. He then removes two fraction 1 over 6 cups of ice cream to share wi
marta [7]
So, he had 2 thirds then removed 2 sixths. You have to subtract the fractions. 

2 sixths is equal to 1 third.

2 thirds-1 third= 1 third.

Grant has 1/3 of a cup of ice cream left in his bowl.

I hope this helped!

Please mark me brainliest!

3 0
2 years ago
A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilog
stellarik [79]

Answer:

C. 98

Step-by-step explanation:

The proposed regression equation is weight = b + width * m

R2 = 0.423

A.) What is the regression equation for this example?

The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963

In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:

^Y= 2.3013 + 0.7963Xi

B.) What is the explanatory, or predictor, variable in this study?

The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:

X: Width of a horseshoe crab (cm)

C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.

To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.

The hypotheses are:

H₀: β=0

H₁: β≠0

α: 0.05

The value of the statistic under the null hypothesis is t= 8.48

D.) What can we say about the p-value?

This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:

P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001

E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?

As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:

Critical values ± = ± = ± 1.984

This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-

F.) Find the confidence interval for the slope.

Using a 95% confidence level, the interval for the slope is:

[m ± Sm]

[0.7963 ± 1.984 * 0.0939]

[0.61; 0.98]

G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.

Yes, there is a significant relationship between the width and weight of the horseshoe crabs.

Using the critical value approach:

The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.

If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.

4 0
3 years ago
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