The z-score for 2,500 g is –2.According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.
2.5% of babies weigh less than 2,500g.
Empirical ruleEmpirical rule states that for a normal distribution, 68% of the values are within 1 standard deviation from the mean, 95% of the values are within 2 standard deviation from the mean and 99.7% are within 3 standard deviation from the mean.
Given that mean (μ) = 3,500 g and a standard deviation of σ = 500 g.
95% of babies have a birth weight of between two standard deviation = 2,500 g and 4,500 gHence 2.5% of babies weigh less than 2,500g.
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Mrs. Smith had 4/6 of a carton of eggs. she dropped a fourth of the eggs. how many eggs was left
First, let's get out common denominators.
8/12 and 3/12.
We then minus the 8 and 3 = 5/12.
We have 5/12.
That's your answer.
A square is increased by 4 inches on each side. If the new area is 36 in^2, what was the length of a side of the original square?.
Answer:
2in
Step-by-step explanation:
Let's call the original side "x". so x² (area of a square) is = x² (as we can't simplify it). Then we got a 4 added to each side. So now we redefine each side as "x+4". So now we can make an equation of the area of the square. x² + 4² = 36. Now you realize that 36 is 6² so you write it. x² + 4² = 6² . Since everything is now a square just square root everything (√) So Now x + 4 = 6. Now you have a 1st degree equation now solve simple math. x = 6 - 4 = 2. The side of original square is 2in
Find the volume of the triangular prism
Answer:
Step-by-step explanation:
Ok so first we need to look and rule out the ones that are not correct like 9m and 5m. ok now we ruled out 2 of the wrong ones and now we have 90m and it looks like a 45m. now we multiply 5 x 2 x 9 which equals 90. so the answer is 90.
Hope it helps!
Answer:
45
Step-by-step explanation:
with triangles you have to do base times height and divide by 2 so 5*9*2=90 and 90 divided by 2 is 45
Select all that apply.
A point located at (5, -2) undergoes two transformations. Its image is located at (-5, 2). What were the transformations?
The point was reflected over the y -axis and translated up 4 units.
The point was translated right 10 units and reflected over the x -axis.
The point was translated left 10 units and up 4 units.
The point was reflected over the y -axis and translated down 4 units.
#1 : reflected over y-axis, so x changes signs and becomes negative (-5, -2)
translated 4 units up, so move the point up 4 units/squares (-5, 2)
#2 translated right 10 units, so the points move right 10 squares (15, -2)
reflected over x-axis, so y changes signs (15, -2)
#3 translated left 10 units (-5, -2)
up 4 units (-5, 2)
#4 reflected over the y -axis (-5, -2)
translated down 4 units (-5, -6)
Answer:
1 and 3
Step-by-step explanation:
Which of the values in the set {2, 3, 4, 5} is a solution to the equation 2x + 4 = 10? (4 points) 2 3 4 5
Answer:2
Step-by-step explanation:
Answer:
Its 3
Step-by-step explanation:
10- 4 = 6
2 x ? = 6
2 x 3 = 6
John has a deck of cards 52 cards of John remove the number to car from the deck what is the probability that he will pick up a number two card at random ?
Answer:
3 out of 51
Step-by-step explanation:
If he removed one number two card from the deck then there should be three left since there are 4 of each number card in a deck so therefore there should be 51 cards in the deck but only three number two cards left in the deck
The probability of drawing a number two card from a 52-card deck after removing all four number two cards is 0, as there are no such cards left to draw.
Calculating the Probability of Drawing a Number Two Card
If John removes the number two card from a standard 52-card deck, the deck then has 48 cards because there are 4 number two cards, one in each suit (clubs, diamonds, hearts, and spades). Since these cards are no longer in the deck, the probability of picking up a number two card at random from the remaining deck is 0, as there are no number two cards left to draw.
Initially, the probability of drawing a two card from a full deck would be 4 out of 52 cards or 1 out of 13, as there are 4 twos in the set of 52 cards. However, with the removal of all four number twos, there are no such cards left, hence the probability of drawing a two is reduced to 0.
Understanding probability in a deck of cards is a fundamental concept in statistics and probability theory, which can be applied to various practical situations including games and predictive models.
In the graph, z is a complex number represented as a vector from the origin. What is the product of z and its conjugate?
Answer:
5
Step-by-step explanation:
Given a complex number x + yi then the conjugate is x - yi
Note the real part remains unchanged while the sign of the imaginary part is negated.
here z = 1 - 2i hence conjugate is 1 + 2i
and the product is
(1 - 2i)(1 + 2i) ← expand factors
= 1 - 4i² [ i² = - 1 ]
= 1 + 4
= 5
The product of z and its conjugate will be 5.
What is a complex number?The complex number is the combination of the real part and the imaginary part. Then the complex number is given as
⇒ a+bi
In the graph, z is a complex number represented as a vector from the origin.
Then the complex number will be
z = 1 – 2i
Then the conjugate of z will be
⇒ 1 + 2i
Then the product of z and its conjugate will be
⇒ (1 – 2i)(1 + 2i)
⇒ 1² – 2²i²
We know i² = -1
⇒ 1 – 4(-1)
⇒ 1 + 4
⇒ 1² – 2²i²
⇒ 5
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Suppose a football is kicked with an initial velocity of 82 ft/sec., at an angle of
58° to the ground. What is the position of the ball after two seconds?
(Remember: Acceleration due to gravity is 32 ft/s².) Round your answer
to the nearest whole foot. Show all work.
Answer:
The position P is:
[tex]P = 87\^x + 75\^y[/tex] ft Remember that the position is a vector. Observe the attached image
Step-by-step explanation:
The equation that describes the height as a function of time of an object that moves in a parabolic trajectory with an initial velocity [tex]s_0[/tex] is:
[tex]y(t) = y_0 + s_0t -16t ^ 2[/tex]
Where [tex]y_0[/tex] is the initial height = 0 for this case
We know that the initial velocity is:
82 ft/sec at an angle of 58 ° with respect to the ground.
So:
[tex]s_0 = 82sin(58\°)[/tex] ft/sec
[tex]s_0 = 69.54[/tex] ft/sec
Thus
[tex]y(t) = 69.54t -16t ^ 2[/tex]
The height after 2 sec is:
[tex]y(2) = 69.54 (2) -16 (2) ^ 2[/tex]
[tex]y(2) = 75\ ft[/tex]
Then the equation that describes the horizontal position of the ball is
[tex]X(t) = X_0 + s_0t[/tex]
Where
[tex]X_ 0 = 0[/tex] for this case
[tex]s_0 = 82cos(58\°)[/tex] ft / sec
[tex]s_0 = 43.45[/tex] ft/sec
So
[tex]X(t) = 43.45t[/tex]
After 2 seconds the horizontal distance reached by the ball is:
[tex]X (2) = 43.45(2)\\\\X (2) = 87\ ft[/tex]
Finally the vector position P is:
[tex]P = 87\^x + 75\^y[/tex] ft
732,178 + 167 - 542,137
Answer:
190,208
Step-by-step explanation:
732,178 + 167 = 732345
732345 - 542,137 = 190,208
190,208
Step by Step
732178+167=732345
732345-542137=190208
Can someone help me with this?
Answer:
Step-by-step explanation:
First triangle is a 45-45-90 triangle. In most basic form, the two equal sides have length 1 and the hypotenuse has length √2. Do not write x√2.
Second triangle: The shortest side is 1, the longer side is √3 and the hypotenuse is 2. You could verify this using the Pythagorean Theorem:
2² = 1² + (√3)² is true.
Please, no more than 2 problems per post. Please re-post the remaining problems and either I or someone else will help you with them.
Fred is trying to earn $35 to buy a basketball. He has saved $11.25. He earns $2.25 per hour doing yard work for his neighbor, and he earns $7.25 per hour selling sunglasses at the mall. Will Fred have enough to buy the basketball if he works in the yard for 2 hours and at the mall for 3 hours? Use the inequality 2.25y + 7.25z + 11.25 ≥ 35.
No, because the total will be $58.75.
No, because the total will be $21.25.
Yes, because the total will be $37.50.
Yes, because the total will be $26.25.
Answer:
Yes, because the total will be $37.50
(cool profile pic)
Step-by-step explanation:
Yes, because the total will be $37.50
David took out a 12-year loan for $68,000 at an APR of 4.1%, compounded
monthly, while Ralph took out a 12-year loan for $98,000 at an APR of 4.1%,
compounded monthly. Who would save more by paying off his loan 5 years
early?
A.David would save more, since he has $30,000 more in principal
B.David would save more, since he has $30,000 less in principal
C.Ralph would save more, since he has $30,000 more in principal
D.Ralph would save more, since he has $30,000 less in principal
Answer:
C.Ralph would save more, since he has $30,000 more in principal
Step-by-step explanation:
The amount of interest each will pay (or save) on his loan is proportional to the amount of principal. Since Ralph's principal of $98000 is more than David's principal of $68000, Ralph will save more by paying off the loan early.
Find the area of the given triangle to the nearest square unit. Angle a= 30 degrees, b=10, angle B=45 degrees
Answer:
[tex]A=34\ units^2[/tex]
Step-by-step explanation:
Suppose we have a general triangle like the one shown in the figure.
We know the angle A, the angle B and the length b.
[tex]A = 30\°\\\\B = 45\°\\\\b = 10[/tex]
By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.
So
[tex]A + B + C = 180\\\\30 + 45 + C = 180[/tex]
We solve the equation and thus we find the angle C.
[tex]C = 180 - 30-45\\\\C = 105[/tex]
We already know the three triangle angles.
Now we use the sine theorem to calculate the sides c and a.
The sine theorem says that:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Then
[tex]\frac{sin(30)}{a}=\frac{sin(45)}{10}[/tex]
[tex]\frac{sin(30)}{\frac{sin(45)}{10}}=a[/tex]
[tex]a=7.071[/tex]
Also
[tex]\frac{sin(105)}{c}=\frac{sin(45)}{10}[/tex]
[tex]\frac{sin(105)}{\frac{sin(45)}{10}}=c[/tex]
[tex]c=13.660[/tex]
Finally, we use the Heron formula to calculate the triangle area
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where s is:
[tex]s=\frac{a+b+c}{2}[/tex]
Therefore
[tex]s=\frac{7.071+10+13.660}{2}[/tex]
[tex]s=15.37[/tex]
[tex]A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}[/tex]
[tex]A=34\ units^2[/tex]
There are 25 betta fish at a pet store. The next day 9 betta were token. How many bettas are left?
Answer:
16 beta fish
Step-by-step explanation:
Take the starting number of fish: 25, and subtract it by the number of fish being taken away: 9.
Answer:
16
Step-by-step explanation:
if we have 25 bettas and then 9 were taken that means we should subtract 9 from 25 to get 16 bettas left
Simplify to create an equivalent expression.
4(6r+3) + 2(r + 2)
plsss i need helppp
To simplify 4(6r+3) + 2(r + 2), distribute the coefficients, combine like terms, resulting in the simplified expression 26r + 16.
To simplify the expression 4(6r+3) + 2(r + 2), we need to distribute the multiplication over the addition inside the parentheses and then combine like terms.
Distribute the 4 into the first set of parentheses: 4 × 6r = 24r and 4 × 3 = 12.
Do the same with the 2 into the second set of parentheses: 2 × r = 2r and 2 × 2 = 4.
Now, combine the individual terms: The expression becomes 24r + 12 + 2r + 4.
Combine like terms (24r and 2r) and constants (12 and 4): 24r + 2r = 26r and 12 + 4 = 16.
The simplified expression is therefore 26r + 16.
which expression is equivalent to sin7pi/6?
A. sinpi/6
B. sin5pi/6
C. sin5pi/3
D. sin11pi/6
The answer choice is D because sin7pi/6 which it’s exact form is -1/2 the only answer choice which the same exact form is D.
For this case we must find an expression equivalent to:
[tex]Sin (\frac {7 \pi} {6})[/tex]
According to the unit circle, [tex]\frac {7 \pi} {6}[/tex] is in the third quadrant and equals 210 degrees.
Then, we must find an expression equivalent to:
[tex]Sin (210) = - \frac {1} {2} = - 0.5[/tex]
We have to:
[tex]\frac{11 \pi} {6}[/tex]
It is in the fourth quadrant and is equivalent to 330 degrees, according to the unit circle.
[tex]Sin (330) = - \frac {1} {2} = - 0.5[/tex]
Answer:
Option D
Which statement best describes the equation x = 3
The equation x = 3 represents a vertical line, but not a linear function, as it violates the definition of a function. Thus, the correct choice is D.
The equation x = 3 describes a vertical line passing through the point where x equals 3 on the coordinate plane.
While it represents a line, it fails to meet the criteria of a function because it violates the one-to-one mapping between inputs (x-values) and outputs (y-values).
For every value of x, the y-value remains constant at 3, meaning multiple x-values map to the same y-value, thus failing the vertical line test for functions.
Therefore, although it represents a line, it does not represent a linear function. Thus, the correct choice is D.
Complete Question:
Which statement best describes the equation x = 3?
A. The equation can not be graphed.
B. The equation represents a function, but not a linear function.
C. The equation represents a linear function.
D. The equation represents a line, but not a linear function.
consider the inequality-5(x+7)<-10 write an inequality representing the solution for x
Answer:
x > -5
Step-by-step explanation:
-5(x+7)<-10
Divide each side by -5. Remember to flip the inequality
-5/-5(x+7)>-10/-5
x+7 > 2
Subtract 7 from each side
x+7-7>2-7
x > -5
The binomial expansion of (x^2+y^2)^2 is
Answer:
x^(4)+2x^(2)y^(2)+y^4)
Hope This Helps! Have A Nice Day!!
The binomial expansion of (x²+y²)² is x⁴ +y⁴ + 2x²y²
What is binomial expansion?The theorem states that any power of a binomial (a + b)ⁿ can be expanded as a specific sum of products (), such as (a + b)² = a² + 2ab + b².
Given
The given expression is (x² + y²)² and we have to simplify it to find the binomial expansion.
(x ²+ y²)² is in the form of (a + b)².
When we expand (a + b)² we get the binomial expression
(a + b)² = a² + b² + 2ab
Now we put the value of a = x² and b = y²
(x² + y²)² = (x²)² + (y²)² + 2(x²)(y²)
= x⁴ + y⁴ + 2x²y²
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What is the measure of a
Answer:
a = 70°
Step-by-step explanation:
a and 110 form a straight angle, thus
a + 110 = 180 ( subtract 110 from both sides )
a = 70°
Answer:
a =70
Step-by-step explanation:
Angle a and 110 are supplementary, which means they add to 180 degrees
a+ 110 = 180
Subtract 110 from each side
a+110-100=180-110
a = 70
67,124 x = ________. Will the product of this equation be less than or greater than 67,124? Explain your reasoning.
Answer:
greater than 67,124
Step-by-step explanation:
since you are multiplying 67,124 with a variable(x) and multiplication only increases the value, the answer is greater than since you are multiplying 67,124 with a variable, which will only increase the product value
help me plz and god bless
Answer:
Step-by-step explanation:
4 (10)
5 (13)
6 (16)
7 (19)
Answer:
On the first picture
1 goes to 16.
2 goes to 13
3 goes to 10
4 goes to 19
On the second picture
1 goes to 9
2 goes to 11
3 goes to 13
4 goes to 15
Help with sectors of circles
Answer:
Step-by-step explanation:
The perimeter is the arc length plus the two radius lines.
Arc length is:
s = (θ/360) 2πr
So the perimeter is:
P = (θ/360) 2πr + 2r
Given that θ=135 and r = 11:
P = (135/360) 2π(11) + 2(11)
P = 8.25π + 22
P ≈ 47.9
So the perimeter is greater than 47.5 cm.
If f(x) = |x – 5| + 3, find f(2).
Answer:
f(2)=6
Step-by-step explanation:
f(x) = |x – 5| + 3 and find f(2). We plug in 2 for x
f(2) = |2 – 5| + 3
f(2) = |-3| + 3 absolute value makes the number inside positive
f(2)= 3+3
f(2)= 6
john runs 15 miles in 3 hours.How many can he run per hour
Answer:
5 miles per hour
Step-by-step explanation:
You divide 15/3 and get 5.
Answer:
5 miles per hour
Step-by-step explanation:
To determine how fast he can run per hour, take the miles and divide by the number of hours
15 miles / 3 hours
5 miles per hour
I have 811 handkerchief in all, and need 25 for one quilt. How many quilts can I make and how many handkerchief will be left over?
Answer:
32 with 11 handkerchief left over
Step-by-step explanation:
Handkerchief = 811
Quits for 1 handkerchief = 25
Number of quits
= 811 ÷ 25
= 32 Remainder 11
Answer:
32 reminder of 11
Step-by-step explanation:
the supplement of an angle whose measure is represented by (5x+35)* has a measure of 2(2x+5)*. Find the measure of the smaller angle.
Step-by-step explanation:
a tank containing 64 gallons lost 6 1/4% of this through leakage how much is remaining is the tank
if we take 64 to be the 100%, how much is 6¼% off of it?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 64&100\\ x&6\frac{1}{4} \end{array}\implies \cfrac{64}{x}=\cfrac{100}{6\frac{1}{4}}\implies \cfrac{64}{x}=\cfrac{\frac{100}{1}}{\frac{25}{4}}\implies \cfrac{64}{x}=\cfrac{100}{1}\cdot \cfrac{4}{25} \\\\\\ \cfrac{64}{x}=16\implies 64=16x\implies \cfrac{64}{16}=x\implies 4=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{it had}}{64}-\stackrel{\textit{leakage}}{4}\implies \stackrel{\textit{remaining}}{60}[/tex]
Answer:
60 gallons of gas remained in the tank.
Step-by-step explanation:
1) 6 1/4 = 6.25
2) 64*6.25% = 4 OR 64*6 1/4 = 4
3) 64 - 4 = 60
which best describes the range of a function
Answer:
The range of a function is the set of all possible output values.
Answer: any numbers along the x axis
Step-by-step explanation:
in the system shown below, what are the coordinates of the solution that lies in quadrant IV? x2+y2=25 x-y2=-5
Answer:
[tex]x=4,y=-3[/tex], or as an ordered pair: (4, -3)
Step-by-step explanation:
We have the system of equations
[tex]x^2+y^2=25[/tex] (1)
[tex]x-y^2=-5[/tex] (2)
Let's solve our system step-by-step:
Step 1. Solve for [tex]y^2[/tex] in equation (1)
[tex]x^2+y^2=25[/tex]
[tex]y^2=25-x^2[/tex] (3)
Step 2. Replace equation (3) in equation (2) and solve for [tex]x[/tex]
[tex]x-y^2=-5[/tex]
[tex]x-(25-x^2)=-5[/tex]
[tex]x-25+x^2=-5[/tex]
[tex]x^2+x-20=0[/tex]
[tex](x+5)(x-4)=0[/tex]
[tex]x+5=0,x-4=0[/tex]
[tex]x=-5,x=4[/tex]
Remember that in the fourth quadrant x is positive and y is negative, so we are taking the positive value of x; in other words [tex]x=4[/tex] (4)
Step 3. Replace equation (4) (the positive value of x) in equation (1)
[tex]x^2+y^2=25[/tex]
[tex]4^2+y^2=25[/tex]
[tex]16+y^2=25[/tex]
[tex]y^2=25-16[/tex]
[tex]y^2=9[/tex]
[tex]y=\sqrt{9} ,y=-\sqrt{9}[/tex]
[tex]y=3,y=-3[/tex]
Since y is negative in quadrant IV, we take [tex]y=-3[/tex]
We can conclude that the solution of our system of equations that lies in the quadrant IV is [tex]x=4,y=-3[/tex], or as an ordered pair: (4, -3)
Answer:
if you type (4,-3) is wrong