[tex]7x +8y = 25 ~~~....(i)\\\\9x +10y = 35~~~ ....(ii)\\\\\text{Multiply equation (ii) by}~ \dfrac 79 ~ \text{and do (ii) - (i):}\\\\\dfrac 79 (9x +10y) - (7x +8y) = \dfrac 79 (35) - 25\\\\\\\implies 7x +\dfrac{70y}9 - 7x -8y = \dfrac{245}9 -25\\\\\\\implies - \dfrac{2y}9 = \dfrac{20}9\\\\\\\implies -2y =20\\\\\implies y =-10\\\\\text{Substitute}~ y = -10~ \text{in equation (i):}\\\\\\7x +8(-10) = 25\\\\\implies 7x = 25 +80\\\\\implies 7x = 105 \\\\\implies x =15\\\\[/tex]
[tex]\\\text{Hence}~ (x,y) = (15,-10)[/tex]
a health status survey in a few villages revelaed that the normal serum protein value of children in that locality is 7.0g/100ml. A group of 16 children, who received high protein food for a period of 6months had serum protein values shown below.Can we consider that the mean serum protein level of these who were fed on high protein is different from that of general population
We can consider that the mean serum protein level of the group of children who received high protein food is different from that of the general population with a normal serum protein value of 7.0g/100ml.
To determine whether the mean serum protein level of the group of 16 children who received high protein food is different from that of the general population with a normal serum protein value of 7.0g/100ml, we can perform a hypothesis test.
Let's denote:
μ1 = Mean serum protein level of the general population (assumed to be 7.0g/100ml)
μ2 = Mean serum protein level of the group fed on high protein food
The null hypothesis (H0) would be that there is no difference between the mean serum protein levels of the two groups:
H₀: μ₁ = μ₂
The alternative hypothesis (Ha) would be that there is a difference between the means:
Hₐ: μ₁ ≠ μ₂
Next, we calculate the sample mean and standard deviation of the group that received high protein food from the given serum protein values.
Assuming the serum protein values (in g/100ml) for the 16 children are as follows:
8.2, 7.6, 7.8, 7.4, 8.0, 7.9, 7.7, 7.5, 7.2, 7.3, 8.1, 7.6, 8.3, 8.0, 7.8, 7.9
Sample mean (x') = (sum of values) / (number of values) = (121.8) / (16) ≈ 7.613 g/100ml
Sample standard deviation (s) ≈ 0.352 g/100ml
Next, we perform a two-sample t-test (assuming equal variances) to compare the means of the two groups. We use the formula:
t = (x'₁ - x'₂) / √[(s₁² / n₁) + (s₂² / n₂)]
where x'₁ and x'₂ are the sample means of the two groups, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.
Substituting the values, we get:
t ≈ (7.613 - 7.0) / √[(0.352² / 16) + (0.0² / 16)] ≈ 3.584
Now, we need to find the critical t-value at a given significance level (commonly set at 0.05) and degrees of freedom (df = n1 + n2 - 2). Since we have 16 + 16 - 2 = 30 degrees of freedom, the critical t-value (two-tailed test) is approximately 2.042.
Since the calculated t-value (3.584) is greater than the critical t-value (2.042), we reject the null hypothesis (H0). This means that there is a significant difference between the mean serum protein levels of the two groups.
In conclusion, based on the given data and the hypothesis test, we can consider that the mean serum protein level of the group of children who received high protein food is different from that of the general population with a normal serum protein value of 7.0g/100ml.
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determine the value of x in each triangle
Answer:
180
Step-by-step explanation:
Subtract the sum of the two angles from 180 degrees.
Answer:
we know that it is 0.6 km
so we convert into meters
and then get 600 m
Hope that helps
Answer:
ok thank u ig
Step-by-step explanation:
12Q. Sweeti covered 2/7 of the running track by walking and rest by running and the length of the track is 630 m. Find the distance covered by running ?
Step-by-step explanation:
Given that :
Total length of the track = 630 m
Distance covered by Sweeti by walking = 2/7 of the running track
2/7 of 630 m
⇛ (2/7)×630
⇛ (2×630)/7
⇛ 1260/7
⇛ 180 m
Distance covered by walking = 180 m
Remaining distance =
Total distance - Distance covered by walking
⇛630 m - 180 m
⇛ 450 m
The total distance covered by running by Sweeti is 450 m.
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Similar Question
You can burn about 450 calories if you run 5 miles. How many miles will you need to run to burn 630 calories? Justify your reasoning.....
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In a regression model of student grades, we would code the nine categories of business courses taken (ACC, FIN, ECN, MGT, MKT, MIS, ORG, POM, QMM) by including nine binary (0 or 1) predictors in the regression. Group startsTrue or False
Binary predictors are simply used to represent dummy variables in regression.
The statement that the nine categories can be coded by nine binary predictors is false.
Binary predictors can only take any of the two binary values (0 and 1).
This means that, the nine categories cannot be represented using binary values or predictors
This is so because, the number of categories (9) is greater than the number of predictors (2).
Hence, the given statement is false
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The product of .010 and .001 is
Answer:
its 0.00001
I hope this helps
2/3 of a cup of batter can make 5/6 of a batch of pancakes. How many cups of water are needed to make one batch of pancakes?
Answer:
1 11/12 cups of water
Consider function f.
Which graph represents function f?
A. W
B. X
C. Y
D. Z
Answer:
W
Step-by-step explanation:
I got a 100% on my test
Each element of X receives exactly one element of Y when a function from one set to the other is used. W graph illustrates the function f.
Explain about the function?
An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
An example of a rule is a function, which yields one output from a single input. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this. There is only one output for y for every input for x. We would say that y is a function of x since x is the input value.
A function is a relationship between a collection of inputs and a set of potential outputs, where each input is connected to exactly one output, in accordance with a technical description.
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Which inequality is true when the value of R is 18? I'ma shower the answers i can choose in the picture
Answer:
See below:
Step-by-step explanation:
Hello! We can check to see if the inequality is true by replacing r with 18 as we have been told to find them in which 18 as r makes the equation true.
So our equations to test for are:
[tex]-r-3>-6\\-r+3<6\\r+3<6\\-r+3>6[/tex]
We can input 18 as r and then we see the following are correct:
1. No, as a -21 is not greater than -6
2. Yes, as -15 is less than 6.
3. No, as 21 is not greater than 6
4. No, as -15 is not greater than 6.
Cheers!
Please can someone help me with this
Answer:
1 : 0.44.
Step-by-step explanation:
93 : 41
= (93/93) : (41/93)
= 1 : 0.44.
Triangle A is a scaled version of triangle B. The dimensions of triangle A are twice the dimensions of triangle B. The area of triangle B is 40.5 sq cm. What is the area of triangle A?
Step-by-step explanation:
the lengths of any line (side, height,...) in A is twice as long as in B.
now, the area of a triangle is
baseline × height / 2
so, two lines are multiplied. that means the factor 2 gets multiplied in 2 times. and that means the area increases by the factor 2×2 = 4
therefore, the area of A is
40.5 × 4 = 162 cm²
13 If CDEF is a rhombus, find m FED.
Answer:
36
Step-by-step explanation:
8x-20=5x+1
-5 -5
3x=-20+1
+20 +20
3x=21
3 3
x=7
8(7)-20
FED=36
In a recent year, 32.4% of all registered doctors were female. If there were 47,400 female registered doctor that year, what was the total number of registered doctors?
Answer:
come, seamen or even spherm
Step-by-step explanation:
basically when the male and female get involved in sexual activity it creates a child through sperm and egg interaction. the fastest sperm wins the race and 68.6% of them are male doctors
If you see this can you answer this question.
Answer:
The last one
Step-by-step explanation:
-4 1/3 is less than -1 3/4 because its farther on the negative side and -1 3/4 is closer to the positive side
Answer of what is QS
Check the picture below.
and let's not forget that the midsegment of a triangle is always half its parallel base.
[tex]\stackrel{midsegment}{AB}=\cfrac{\stackrel{base}{QS}}{2}\implies 16=\cfrac{QS}{2}\implies 32=QS[/tex]
Two polygons are similar. The corresponding angles of the polygons are- A congruent B proportional C regular D similar
9514 1404 393
Answer:
A congruent
Step-by-step explanation:
In similar polygons, corresponding sides are proportional, and corresponding angles are congruent.
On a map, 1 inch equal 11.7 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?
Answer:
29.25 miles
Step-by-step explanation:
We can use a ratio to solve
1 inch 2.5 inches
------------ = ----------------
11.7 miles x miles
Using cross products
1 * x = 11.7 * 2.5
x =29.25
What determines whether a relationship
is proportional or not?
Answer:
When two ratios exhibit the same connection, they are said to be proportionate. Two ratios may be tested for proportionality by writing them as fractions and then reducing them to the smallest possible number. In this case, your ratios are proportionate since the reduced fractions are the same.
Step-by-step explanation:
Hope it helps:)
help any body plzs i will give brianlyest
- BRAINLIEST answerer
P(x<=30) = 1- exp ( - 30/3600 * 90) = 1- exp (-0.75)
Answer:
(
≤
3
0
)
=
1
−
(
−
3
0
3
6
0
0
⋅
9
0
)
=
1
−
(
−
0
.
7
5
)
Find the domain of the function
Answer:
Here you go :)
Step-by-step explanation:
The diagram below shows two parallel lines, m and n, cut by a transversal, k. Angles A, B, and C are shown in the diagram
A student writes a proof to show that the corresponding angles, A and B, are congruent. The student's proof is shown below
A. Both reason 2 and Reason 3 are correct as shown in the table
B. Reason 2 is correct, but Reason 3 should "Alternate interior angles are congruent"
C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct
D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent"
(look at picture to understand better)
9514 1404 393
Answer:
B
Step-by-step explanation:
Angles A and C are vertical angles; angles B and C are alternate interior angles. Only line 3 of the proof is in error.
The applicable description is found in choice B.
solve pls brainliest
Answer:
4/12 > simplified to > 1/3
Step-by-step explanation:
hope it helps
Sally must have at least $200 in her savings account to avoid a
fee. She currently has $850 in her account, but plans to spend
$75 per week. Write an inequality to determine the number of
weeks she can spend money and avoid a penalty.
Answer:
675$
Step-by-step explanation:
got it right
Calculate: 7×9-22+31=
Answer:
72
please mark brainlest
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
7x9=63
63-22=41
41+31= 72
Hope this helps
Pls help. The question is on the picture
Answer:
23518
Step-by-step explanation:
1) the total volume can be calculated as the sum of two volumes (for more info see the picture): V=V₁+V₂, where V₁ belongs to the prisma and V₂ - to the cylinder;
2) V₁=a*b*h; V₁=20*20*37=14800 (m³);
V₂=3/4*(π*r²*h); V₂=3/4*3.1415*100*37≈8717,6625 (m³), note the full volume of the cylinder cannot be included into the result, but 3/4 of its volume;
3) finally, V=14800+8717.6625=23517,6625≈23518 (m³).
Answer:
V = 23518 m3
Step-by-step explanation:
The volume of the cube part of building
(20)(20)(37)=14800 cm3
Each cylinder:
h=37/12=3.083 m
r=10 m
[tex]v=\pi (10)^{2} (3.083)=968.66m^{3}[/tex]
all the cylinders:
[tex]v=(12)(968.66)=11,623.89cm^{3}[/tex]
Total volume.
[tex]V=14800+\frac{3}{4} (11,623.89)[/tex]
[tex]V=14800+8717.92=23,517.92[/tex]
nearest m3:
[tex]V=23518m^{3}[/tex]
I hope this help you
in the Sahara desert one day it was 136°F in the gobi desert a temperature of -50°F was recorded what is the difference between these two temperatures
Answer:
186 °F
Step-by-step explanation:
The difference is found by subtracting the smaller from the larger:
136 -(-50) = 136 +50 = 186
The difference between the two temperatures is 186 °F.
Pre college need help
Answer:
C
Step-by-step explanation:
A force of 56N is required to keep a spring stretched 4m from the equilibrium position. How much work in Joules is done to stretch the spring 8m from equilibrium? Round your answer to the nearest hundredth if necessary.
Please check the attached images for the answer. Answer with full explanation is screenshoted. Plz refer.
Thanks ☺️
Hope it helps you.
Helpppppppppppppppppppppppppppp
Answer:
look at the photo...............