The mean mark of the girls is 86.
How is the mean mark calculated?You must first add up all the numbers (3 + 11 + 4 + 6 + 8 + 9 + 6 = 47) before you can determine the mean. The amount is then divided by the number of scores utilized (47 / 7 = 6.7).
Given information:
The number of total students in the class is 30
Given number of boys in the class is 20
Then, the number of girls will be = 30-20
=10
The mean mark of the class = 70×30
= 2100
The guy's average grade is = 62.
Then, mark for the boys = 62×20
= 1240
The mark for the girls = 2100-1240
= 860
Then the mean mark of the girls will be =860/10
= 86
Hence, the mean mark for the girls is 86
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15-5 Similar Figures and ProportionsNLesson Quiz: Part 11. Identify the correspondingsides in the pair of triangles,and use ratios to determine 14 cmwhether the triangles aresimilar.12 cm4 cm7 cmR56 cmPOLook at Slide 19.Identify the corresponding sides in the pair of triangles, and use ratios to determine whetherthe triangles are similar.(50 Points)SimilarNotSimilar
In order to identify if the triangles are similar, you first take into account the rect angle of the triangles. Form there you can notice that side ON in the bigger triangle, is similar to the side as RQ in the little one.
So, you calulate the proportion between sides ON and RQ, just as follow:
[tex]\frac{ON}{RQ}=\frac{8cm}{4\operatorname{cm}}=2[/tex]Then, the proportion of those sides is 2. This proportion must be the same for the other similar sides of both traingles, in order to conclude that the triangle are similar.
[tex]\frac{PN}{QS}=\frac{14\operatorname{cm}}{7\operatorname{cm}}=2[/tex][tex]\frac{PO}{RS}=\frac{12\operatorname{cm}}{6\operatorname{cm}}=2[/tex]Hence, the triangles are similar
A student was asked to find the length of the unknown leg of the right triangle. He incorrectly said that the length of the unknown leg of the right triangle is about 6.2 cm. Find the length of the unknown leg of the right triangle.The length of the unknown leg of the triangle is ______cm. (Round to one decimal place as needed.)What mistake might the student have made? A. He added the two given valuesB. He subtracted the two given values C. He did not square the length of the given leg D. He did not square the length of the hypotenuse
6 cm, C. He did not square the length of the given leg
Explanation
to solve this we need to use the Pythagorean theorem
T.P states for all rigth triangles:
[tex]a^2+b^2=c^2[/tex]then
Step 1
let
a=2.3
b=b
c=6.4
replace
[tex]\begin{gathered} 2.3^2+b^2=6.4^2 \\ \text{now, we n}eed\text{ isolate b} \\ 5.29+b^2=40.96 \\ \text{subtract 5.29 in both sides} \\ 5.29+b^2-5.29=40.96-5.29 \\ b^2=35.67 \\ \text{square root in both sides} \\ \sqrt[]{b^2}=\sqrt[]{35.67} \\ b=5.97 \\ \text{rounded} \\ b=6 \end{gathered}[/tex]Step 2
What mistake might the student have made?
check
A)He added the two given values
[tex]2.3+6.4=8.7[/tex]B) He subtracted the two given values
[tex]6.4-2.3=4.1[/tex]C)He did not square the length of the given leg
[tex]\begin{gathered} 2.3^{}+b^2=6.4^2 \\ b^2=6.4^2-2.3 \\ b^2=38.66 \\ b=\sqrt[]{38.66} \\ b=6.21 \\ \text{rounded} \\ b=6.2 \end{gathered}[/tex]D. He did not square the length of the hypotenuse
[tex]\begin{gathered} 2.3^2+b^2^{}=6.4 \\ b^2=6.4-2.3^2 \\ b^2=1.11 \\ b=\sqrt[]{1.11} \\ b=1.05 \end{gathered}[/tex]so, the answer is C
I hope this helps you
The revenue equation for a certain brand of toothpaste is y = 2.2x, where x is the number of tubes of toothpaste sold andy is the total income for selling x tubes. The cost equation is y = 0.6x + 2000, where x is the number of tubes of toothpastemanufactured and y is the cost of producing x tubes. The following set of axes shows the graph of the cost and revenueequations. For what x-values will the company make a profit?
step 1
equate the revenue and the cost
so'
2.2x=0.6x+2000
solve for x
2.2x-0.6x=2000
1.6x=2000
x=1,250
step 2
the company will make a profit when the revenue is greater than the cost
therefore
the value of x must be greater than 1,250
x> 1,250 tubes of toothpaste
Note: For x=1,250 ----> the revenue is equal to the cost (Profit 0)
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The point of maxima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
Given that,
Initial height of the launching pad is 4 feet,
Initial velocity of rocket is 48 feet/sec,
Height of the rocket as a function of time, h(t) = -16t² + 48t + 3
In order to find the time for maximum height equate h'(t) = 0 as follows,
-32t + 48 = 0
⇒ t = 48 / 32
⇒ t = 3 / 2
⇒ t = 1.5
To find the maximum height find h(t) for t = 1.5 as follows,
h(1.5) = -16 × 1.5² + 48 × 1.5 + 3
= -36 + 60 + 3
= -36 + 63
= 27
Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.
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what are two ways that you can present 27 using 3
The two ways that you can represent 27 using 3 are; 3 * 3 * 3 and 3³
How to express factors of a number?A factor of a number is a number or algebraic expression that divides another number or expression evenly.
Now, 3 is a factor of 27 and since we want to represent 27 using only 3, one way to do it is; 3 * 3 * 3 = 27.
Now, in laws of exponents, we know that;
y² = y * y
and y³ = y * y * y
Thus, another way to represent 27 with only 3 using laws of exponents is; 3³ = 27
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a, b, and c represent three different numbers. each is chosen from the set 3 5 7 9 . what is the least possible value of a/b+c?
the larger the denominator compared to the numerator, the smaller the number, so:
[tex](b+c)\gg a\Rightarrow\frac{a}{b+c}\to0[/tex]So, let's choose the smallest number as a numerator, and the biggest numbers as a denominator:
[tex]\frac{3}{7+9}=\frac{3}{16}=0.1875[/tex]If the simple interest on a $5,000 for 8 years is $2,000, then what is the interest rate?
Given data:
The principal is
[tex]P=\text{ \$5,000}[/tex]The time is
[tex]t=8[/tex]The interest is
[tex]=\text{ \$2,000}[/tex]Concept:
The formula to calculate interest rate (R) is given below as
[tex]\begin{gathered} I=\frac{P\times R\times T}{100} \\ 100I=P\times R\times T \\ divide\text{ both sides by PT} \\ R=\frac{100I}{PT} \end{gathered}[/tex]By substituting the values in the formula above, we will have
[tex]\begin{gathered} R=\frac{100I}{PT} \\ R=\frac{100\times2000}{5000\times8} \\ R=\frac{200000}{40000} \\ R=5 \end{gathered}[/tex]Hence,
The final answer is 5%
A $10 T-shirt is on sale for $4. What is the percent of the discount?
Answer:
The t-shirt is 60% off.
Step-by-step explanation:
If the t-shirt cost ten and is on sale for $4, then the t-shirt is sold for 6/10 less. 6/10=60%. The t-shirt is 60% off.
1) Eliminate one of the variable terms on one side of each multi-step equation: Multi-Step Equation 7a-6=7+ 2a 11 - 3b = 3b + 4 -2b-5=6 - 5b Equivalent Two-Step Equation
Answer:
Step-by-step explanation:lol
Find the measure of each angle indicated.
Answer:
Step-by-step explanation:
11: 180-133= 47 degrees
12: 72 degrees
13: 15x+5+(-1+7x)=180
15x+5-1+7x=180
22x+4=180
22x=176
X=8
14: 180-45= 135
14x-5=135
14x=140
x=10
Hopes this helps please mark brainliest
find the counterexample to show that the statement is incorrect the difference of any two counting numbers will be a counting number.a: 7-4=3, which is not a counting numberb: 3-5=-2 which is not a counting numberc: 10-2=8 which is a counting numberd: there is no counterexample the statement is correct
The counting number are the integers that are used for counting like 1, 2, 3, 4, 5...
The number -2 is not a counting number therefore, the difference between 3 and 5, which are counting numbers is not a counting number. The answer is b.
Explain/show how would solve -7-5+7 to lazy to solve it
we have
-7-5+7=-5
because we have -7 and 7 we only left the other number as the result
19. Write an equation of a parabola that opens to the left, has a vertex at the origin, and a focus at (-4, 0).Tava
We have the next information
Parabola that opens to the left
Vertex a the origin (0,0)
Focus (-4,0)
then we will have the next form for the equation of the parabola
[tex]y^2=4px[/tex]where p is -4
[tex]\begin{gathered} y^2=4(-4)x \\ y^2=-16x \\ \end{gathered}[/tex]therefore if we isolate the x we obtain
[tex]x=-\frac{1}{16}y^2[/tex]PLS HELP THIS IS DUE TOMORROW ITS RATIONAL NUMBERS AND I NEED A EXPLANATION ON HOW TO DO IT PLS HELP
Answer:
[tex]\frac{7}{16}=0.4375[/tex]Step-by-step explanation:
To write a fraction as a decimal, you need to divide the numerator by the denominator.
[tex]\frac{7}{16}[/tex][tex]\frac{7}{16}=0.4375[/tex]2. Use the distributive property to expand 0.05(50 + 40). (2 POINTS
100 BRAINLY POINTS FOR WHOEVER ANSWERS
Answer:
4.5
Step-by-step explanation:
Answer:
4.5
Step-by-step explanation:
help pleasee!!! A quick answer would be greatly appreciated
In first question, the value of Angle 1 is 42 and the value of Angle 2 is 48.
In second question, the value of Angle 1 is 11, Angle 2 is 159, Angle 3 is 11, Angle 4 is 165.
In the given question, have two question.
Firstly solving the question 1.
1) In question 1 we have to find the measure of Angle 1 and Angle 2.
There is figure. In this figure we can see that it is a right angle.
The right angle is of 90 degree.
So x+x+6=90
Simplifying the expression
2x+6=90
Subtract 6 on both side
2x+6-6=90-6
2x=84
Divide by 2 on both side
2/2x=84/2
x=42
The value of x is 42.
Now The value of Angle 1 is 42.
Now finding the Angle 2.
Angle 2 is x+6 and x=42
So
=42+6
=48
Hence, the value of Angle 2 is 48.
2) In this question we have to find the value of Angle 1,2,3 and 4.
To solve this question we using the straight line angle.
As we know that the angle of straight angle is 180.
So from the figure we can see that
∠2+∠3=180
As we know that ∠3=2x+3
So ∠2+2x+3= 180
Subtract 3 on both side
∠2+2x+13−13=180−13
∠2+2x=167................Equation 1
As we can also know from the figure that
∠1+∠4=180
And ∠1=x+7
x+7+∠4=180
Subtract 7 on both side
x+7+∠4−7=180−7
∠4+x=173.......................Equation 2
From the corresponding angle theorem we know
∠1=∠3
2x+3=x+7
Subtract 3 on both side
2x+3−3=x+7−3
2x=x+4
Subtract x on both side
2x−x=x+4−x
x=4
Now putting the value of x in Equation 1
∠2+2x=167
∠2+2×4=167
∠2+8=167
Subtract 8 on both side
∠2+8−8=167−8
∠2=159
Now putting the value of x in Equation 2
∠4+x=173
∠4+4=173
∠4+4=173
Subtract 4 on both side
∠4+4−4=173−8
∠4=165
∠3=2x+3
∠3=2×4+3
∠3=8+3
∠3=11
∠1=x+7
∠1=4+7
∠1=11
Hence, the value of Angle 1 is 11, Angle 2 is 159, Angle 3 is 11, Angle 4 is 165.
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here is the 4rth one to do
The correct option is; Yes, all the three expressions are equivalent to each other.
What is meany by the term exponent?A number's exponent signifies how many times a number has been multiplied by itself. For instance, 2×2×2×2 can be written as 2⁴, because 2 is multiplied on its own four times. In this case, 2 is referred to as the "base," and 4 is referred to as the "exponent" as well as "power." In general, xⁿ denotes that x has been multiplied by itself n times.For the given question;
The three expressions are given as;
a: 20(1.1ˣ) ...1
b: 20(1.1⁻¹)⁻¹ˣ
Simplifying as;
= 20(1.1⁻¹⁽⁻¹ˣ⁾)
= 20(1.1ˣ) ....2
c: 20(1.1¹/⁵)⁵ˣ
Simplifying.
= 20(1.1¹/⁵⁽⁵ˣ⁾)
= 20(1.1ˣ) ....3
So, a = b = c
Thus, all three expressions are equivalent to each other.
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4 out of every 6 tudent have brown eye if there are 150 tudent what b the number of tudent who have brown eye
If there are 150 students then the number of students that have brown eyes is 100 students .
In the question ,
it is given that ,
that 4 students out of every 6 student have brown eyes ,
So , the percent of boys that have brown eyes = (4/6) × 100
= 66.66%
So , 66.66% of the students have brown eyes .
So , in 150 students ,
the number of students that have brown eyes = 66.66% of 150
= (4/6) × 150
= 4 × 25
= 100
So , 100 students have brown eyes .
Therefore , If there are 150 students then the number of students that have brown eyes is 100 students .
The given question is incomplete , the complete question is
4 out of every 6 student have brown eyes if there are 150 student . what is the number of student who have brown eye ?
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It is believed that the best angle to fly a kite is 45°. If you fly a kite at this angle and let out 190 feet of string, approximately how high above the ground will the kite be?
Triangle MNO is similar to triangle PQR. Find the measure of side PQ. Round your answer to the nearest tenth if necessary. R 11 M 45 4.6 M Р Answer: Submit Answer here to search
Answer: PQ = 18.8
The right angle triangles are similar
ON = QR
MN = PQ
Step 1: Establish the similarity theorem
[tex]\begin{gathered} \frac{ON}{QR}\text{ = }\frac{MN}{PQ} \\ \frac{11}{45}\text{ = }\frac{4.6}{PQ} \\ \text{Cross multiply} \\ 4.6\cdot\text{ 45 = 11x PQ} \\ 207\text{ = 11PQ} \\ \text{Divide both sides by 11} \\ PQ\text{ = }\frac{207}{11} \\ PQ\text{ = 18.8} \end{gathered}[/tex]Simplify (4+2i)(1+5i)
The simplyfied expression is: -6 + 22i
To multiply two complex numbers, we need to apply distributive propiertie with each term of each parentheses. In this case:
[tex]\mleft(4+2i\mright)\mleft(1+5i\mright)=4\cdot1+4\cdot5i+2i\cdot1+2i\cdot5i[/tex]Now we can solve:
[tex]4+20i+2i+(2\cdot5)i^2[/tex]i^2 is (-1). Then:
[tex]\begin{gathered} 4+22i+10(-1) \\ 4-10+22i \\ -6+22i \end{gathered}[/tex]-6+22i is the simplified expression
what is negative 3 times 67
Negative 34 means (-34)
times means to multiply, then
[tex]-34\times1567[/tex]To do it without a calculator we will make -34
-30 + -4, then multiply -30 by 1567 and multiply -4 by 1567 then add the two answers
[tex]-4\times1567=-6268[/tex][tex]-30\times1567=-47010[/tex]Then add the answers
[tex]-34\times1567=-6268+-47010=-53278[/tex]The answer is -53278
Answer:
Step-by-step explanation:
-3 times 67 is is minus 207 or -207
write interval notation x>2 or -x >6
To answer this question, we need to have into account the following:
1. In the context of interval notation, the word "or" can be represented by the symbol "U".
2. We need to rearrange the inequality -x > 6 in a way that we have positive x.
We can proceed as follows:
Case x>2[tex]x>2\Rightarrow(2,\infty)[/tex]We can express the inequality in this way because it expresses all of the values greater than 2, and these values tend to the positive infinity. We have parenthesis here since the values are not equal to 2 (only greater than 2).
Case -x > 6If we multiply both sides of the inequality by -1, we need to reverse the direction of the inequality as follows:
[tex]\begin{gathered} -1(-x>6)=-1(-x)<-1(6) \\ x<-6 \end{gathered}[/tex]Now, we have all of the values less than -6, not equal, and because of this, we have to use parenthesis:
[tex]x<-6=(-\infty,-6)[/tex]Therefore, we can say that:
[tex]\begin{gathered} x>2\text{ or -x>6} \\ \end{gathered}[/tex]Can be expressed in interval notation as:
[tex](-\infty,-6)\cup(2,\infty)[/tex]In summary, the answer to this question is:
[tex](-\infty,-6)\cup(2,\infty)[/tex]Multiply (x-4)².
Please help me
⇒ x-4 is the term in this case there for the term (x-4) is squared meaning the term has to multiply itself twice.
[tex]=(x-4)(x-4)\\=x(x-4)-4(x-4)\\=x^{2} -4x-4x+16\\=x^{2} -8x+16[/tex]
If you are still struggling on how to multiply out DM ASAP.
y= -6x^{2} -36
what would it be in vertex from
The vertex form of a parabola is represented by the equation y = -6 (x-0)² -36 -0.
What is a vertex form?
And this equation gives you the vertex of a parabola. h is removed from and k is inserted in the vertex form equation. We can calculate h and k from the equation. The value of h is -b/2a. It is an alternate way of writing out the vertex form. In vertex form, we use the process of completing a square. A quadratic function can also be easily solved algebraically in the vertex form (if it has a solution). Completing the square, also known as converting a quadratic function from standard form to vertex form, is the first step in solving an equation.
The given equation is y = -6x² -36
So, a= -6, b = 0, c = -36
The general formula for the vertex form is given by
y = a[x - (-b/2a))² + c - b²/4a
y = -6((x - (-0/2(-6)))² + -36 - 0²/4(-6)
y = -6 (x-0)² -36 -0
Therefore, the vertex form is y = -6 (x-0)² -36 -0.
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Determine the intercepts of the line.
Do not round your answers.
-7x-6y=-15−7x−6y=−15
I can't figure it out...
The intercepts of the line are( −7/6),( −[tex]\frac{7}{6}x+\frac{5}{2}[/tex]).
How to determine the intercepts of the line?The term "intercept" refers to the location where a line or curve intersects an axis on a graph. An object's x-intercept is defined as where a point crosses the x-axis. The term "y-intercept" refers to a point that crosses the y-axis. The intersection of the x-axis and the y-axis is what is meant by a line's intercept.
Use the slope-intercept form y=mx+b to find the slope m.
7x-6y=-15
m=−7/6.
Use the slope-intercept form y=mx+b to find the slope m.
−7x−6y=−15
m = −[tex]\frac{7}{6}x+\frac{5}{2}[/tex]
The term "intercept" refers to the location where a line or curve intersects an axis on a graph.
The intercepts of the lineare( −7/6),( −[tex]\frac{7}{6}x+\frac{5}{2}[/tex]).
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Which interva notation represents the set of all numbers greater than or equal to -11 and less than or equal to -2? O [-11, -2] O (-11, -2] Submit Answer Of-11, -2) 0 (-11, -2)
When using interval notation a "[" represents that the number belongs to the interval and a "(" means that the number doesn't belong to the interval, it only limits it. On this case we need to find the interval where the numbers are greater or equal to -11, therefore this number belongs to the interval, and less or equal to -2, this number also belongs to the interval. They belong to the interval, because there is "or equal" on the signals. Therefore the interval can be represented as:
[tex]\lbrack-11,-2\rbrack[/tex]Determine whether each statement is true or false: The reason that trig ratios work is because all right triangles are congruent [ Select ] You can find sine, cosine, and tangent from all angles in a right triangle, including th angle (Select] The sine of one acute angle is the cosine of the other acute angle in any right triang [ Select] Tangent is the only trig ratio that can have a value larger than 1 [ Select]
Use a calculator to find the value of each trigonometric function evaluated at their corresponding angles, up to 3 decimal places:
[tex]\begin{gathered} \cos (58)=0.530 \\ \cos (88)=0.035 \\ \tan (50)=1.192 \\ \tan (20)=0.364 \end{gathered}[/tex]….: 5 : 6 : 7= 24 :15 : …. :…. What is the missing number?
Step-by-step explanation:
3×5 = 15
so, the first number n×3 = 24, n = 8
an and then we have
8 : 5 : 6 : 7 = 24 : 15 : 18 : 21
Solve on the interval (0,2%): (sin x + 1)2 sin x-3 sinx-2) = 0 O A. x = 7T,X = 2 x=51 O 3 7T O В. x= N ***= 7+ x = 117 6 6 T T o C. X=2.7 x= 3 O D. x=2x-x-5 2 * = 4
Given:
(sinx + 1)(2sin²x - 3sinx - 2) = 0
sinx + 1 = 0
sinx = -1
Take the arcsin of both-side
x = sin⁻' (-1)
x = -90= -90 + 360 = 270 = 3π / 2
x =3π / 2
Similarly,
2sin²x - 3sinx - 2 = 0
let y = sinx
2y² - 3y - 2 = 0
Factorising the above;
2y² - 4y + y - 2 = 0
2y(y-2) + 1(y-2) = 0
(2y+1)(y-2) = 0
Put sin x back in for y so we can see what it's really supposed to be.
(2sinx + 1 )(sinx -2) = 0
Either one of the terms 2sin x + 1 or sin x - 2 can be 0 for this equation to be true. Let's solve each of them separately.
2sinx + 1 = 0
2sinx = -1
sinx = -1/2
Take the arcsin of both-side.
x= sin⁻' (-1/2)
x = - 30 = -30+360 = 330 ,
x = 7π /6 or 11π/6
Therefore, the correct option is B. x= 3π / 2 , 7π /6 , 11π/6