On evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.
What is Expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. For example -
5x + 7 = 6
7r + π = 4
Given is the following expression -
7.5 + (4² − 2³) ÷ 4
The given expression is -
7.5 + (4² − 2³) ÷ 4
Using the BODMAS rule, we can solve -
7.5 + (16 - 8) ÷ 4
7.5 + 8 ÷ 4
7.5 + 2
9.5
Therefore, on evaluating the given expression 7.5 + (4² − 2³) ÷ 4, we get 9.5 as the result.
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I really need help with this question
Answer:
a) 625; 625; right triangle
b) 205; 256; obtuse triangle
Step-by-step explanation:
The squares are values found in your memory or using a calculator. It is straightforward addition to find their sum.
left side7² +24² = 49 +576 = 625
25² = 625
The sum of the squares of the short sides is the square of the long side, so this is a right triangle.
__
right side6² +13² = 36 +169 = 205
16² = 256
The long side is longer than is needed to form a right triangle, so the largest angle is more than 90°. This is an obtuse triangle (as shown).
Find the value of z.
7
Х
3
Z
Z =✓[?
Applying the leg rule, the value of z in the right triangle given is: √30 units.
What is the Leg Rule?The leg rule states that, hypotenuse/leg = leg/part.
Given the following:
Leg = z unitsPart = 3 unitsHypotenuse = 3 + 7 = 10 unitsPlug in the values into the leg rule:
10/z = z/3
z² = (10)(3)
z² = 30
z = √30 units
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Write an equation in slope intercept form of the line
Answer: y=-1/4x+4
Step-by-step explanation:
slope goes down 1, and right 4 so it's -1/4. Y-intercept is positive 4 so it will be +4
Determine the following probabilities. Enter your final answers as reduced fractions. Two coins are flipped. Find the probability that the first coin land on heads and the second coin lands on heads. Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is black and the second card is a 8. A single digit between 0 and 9 is randomly chosen, and a single letter from A to Z is randomly chosen. Find the probability that the number is 4 and the letter is a consonant. Two dice are rolled. Find the probability that first die lands on an even number and the second die is less than 2.
The probability of an event occurring is given by the ratio of the number of
possible outcome to the number of required outcome.
First question: The probability that the first coin lands on heads and the second coin lands on tails is 0.25.Second question: The probability of drawing a black card and then a 8 is [tex]\underline{\dfrac{1}{13}}[/tex].Third question: The probability that the number chosen is 4 and the letter chosen is a consonant, is [tex]\underline{\dfrac{21}{234}}[/tex].Fourth question: The probability that the first die lands on an even number and the second die is less than 2, is [tex]\underline{\dfrac{1}{12}}[/tex].Reasons:
First question:
The number of faces in a coin = 2; A head or a tail
The probability that the first coin lands on heads, P(H) = [tex]\dfrac{1}{2}[/tex]
The probability that the second coin lands on tails, P(T) = [tex]\dfrac{1}{2}[/tex]
The probability that the first coin lands on heads and the second coin lands
on tails = P(H ∩ T)
Which gives;
[tex]P(H \cap T) = \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}[/tex]
The probability that the first coin lands on heads and the second coin lands on tails = [tex]\dfrac{1}{4}[/tex] = 0.25
Second question:
The number of black cards in a pack of 52 = 26 cards
The number of cards that are a 8 in a pack of 52 cards = 8 cards
[tex]\mathrm{The \ probability \ of \ drawing \ a \ black \ card}, \ P(B) = \dfrac{26}{52} = \dfrac{1}{2}[/tex]
[tex]\mathrm{The \ probability \ of \ drawing \ a \ 8,} \ P(8) = \dfrac{8}{52} = \dfrac{2}{13}[/tex]
The probability of drawing a black card and then an 8, P(B∩8), is given as follows;
[tex]P(B \cap 8) = \dfrac{1}{2} \times \dfrac{2}{13} = \dfrac{1}{13}[/tex]
The probability of drawing a black card and then a 8 is P(B∩8) = [tex]\underline{\dfrac{1}{13}}[/tex]
Third question:
The probability that a number chosen between 0 and 9 is 4, P(4) = [tex]\dfrac{1}{9}[/tex]
The number of consonant in the alphabet = 21
The probability that a letter chosen from A to Z is a consonant, P(C) = [tex]\dfrac{21}{26}[/tex]
The probability that the number chosen is 4 and the letter chosen is a consonant, P(4 ∩ C) = [tex]\dfrac{1}{9} \times \dfrac{21}{26} = \underline{ \dfrac{21}{234}}[/tex]
Fourth question:
The number of even numbers on a die = 3; (2, 4, 6)
The number of numbers less than 2 on a die = 1
The probability that the first die lands on an even number, P(E) = [tex]\dfrac{3}{6}[/tex]
The probability that the second die is less than 2. P(<2) = [tex]\dfrac{1}{6}[/tex]
Therefore;
The probability that the first die lands on an even number and the second die is less than 2, P(E ∩ <2) = [tex]\dfrac{3}{6} \times \dfrac{1}{6} = \dfrac{3}{36} = \underline{\dfrac{1}{12}}[/tex]
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The temperature of a substance in an experiment changes by 8.7F from 10 am to 1p.m. At 5p.m., the temperature is 33.5°F. It
is 2/3 of what the temperature was at 1p.m.
What was the temperature at 10 a.m. of the substance?
Enter your answer as a decimal in the box
Answer:
138
Step-by-step explanation:
A 4-mile cab ride cost $5.50, and a 9 mile cab ride costs $8.00. Identify two points from this information. Let the total cost of the cab ride represent (y) and the number of miles traveled (x)
Two points which can be identified from this information are; (4, 5.50) and (9, 8.00).
According to the question;
total cost of the cab ride represent (y) and the number of miles traveled (x).In essence, the information provided can be used to provide two points as follows; (4, 5.50) and (9, 8.00).
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What is the average rate of change of the function f(x)=120(0. 1)x from x = 0 to x = 2? Enter your answer, as a decimal, in the box. Do not round your answer.
The average rate of change of the function is -59.4
The formula for calculating the rate of change of the function is expressed as:
[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]
Given the function
[tex]f(x)=120(0.1)^x\\f(0) = 120(0.1)^0\\f(0)=120\\[/tex]
Get the value of f(2)
[tex]f(2)=120(0.1)^2\\f(2) = 120(0.1)^2\\f(2)=1.2\\[/tex]
Substitute into the formula to have:
[tex]f'(x)=\frac{1.2-120}{2-0}\\f'(x)=\frac{118.8}{2} \\f'(x)= -59.4[/tex]
Hence the average rate of change of the function is -59.4
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If the original quantity is 15 and the new quantity is 19, estimate the percent change.
15 to 19 was about a 27% in increase
Jan is looking for similar figures. Which choice is similar to the figure shown?
Bottom left as it's measurements and shape are the closest to the one Jan has
The perimeter of the table shown is 16 feet. Write an equation in the form px+q=r to solve for x.
p = 2
q = 6
r = 16
x = 5 feet
Step-by-step explanation:
The perimeter of the rectangle is
In your case,
Width = 3 feet
Length = x feet
So, the perimeter is
Since the perimeter is 16 feet, we have
Hence,
p = 2
q = 6
r = 16
Solve this equation for x:
8+w/4 when w is 16
plz answer it for me plzzz
Answer:
8+w/4 Putting w = 168+16/4(32+16)/4= 48/4= 12Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
what is the discriminant of f(x)=2x^2+8x+16
and the number and type of roots
Answer:
2 imaginary roots
Step-by-step explanation:
The discriminate is the portion of the quadratic equation under the square root
D = b^2 - 4ac
D = 8^2 - 4(2)(16)
D = 64 - 128
D = -64
Since the discriminate is negative the square root will be imaginary
and there will be 2 of them
2 imaginary roots
9514 1404 393
Answer:
discriminant: -64two complex rootsStep-by-step explanation:
The discriminant of ax² +bx +c = 0 is b²-4ac. Here, we have ...
a=2, b=8, c=16
so, the discriminant is 8² -4(2)(16) = 64 -128 = -64
A negative discriminant indicates there are two conjugate complex roots.
What is the slope of the line shown on the graph to the right?
The LEADING COEFFICIENT OR THE LEADING TERM of 3x - 5x^2y^3 + 6xy + 7 is
A)3x
B) - 5x^2y^3
C)5x^2y^3
D) 6xy
NONSENSE=REPORT
The leading term is the term with the highest degree (highest exponent number). Here, the leading term is =》B) - 5x²y³
³ is the highest degree in the given expression.
_____
Hope it helps ⚜
Find the value of z
Answer:
z = 9 I think
Step-by-step explanation:
Because I did the quiz
What's ( Round to the indicated place value
1. 6085 to the nearest hundred
2. 51,672 to the nearest ten thousand
3. 321.6396 to the nearest thousand)
Answer:
I'm not going to give the answer yet to see if you can figure it out.
Step-by-step explanation:
1. Find the place that your are rounding to. Ex: 6085
2. Then, look "nextdoor"; the number to the right of the number underlined. Ex: 6085
3. If this number is 1-4, then keep it the same. If it is 5-9, then add one to the digit to the left. Ex: 6085 becomes 6185
4. All of the digits to the right stay the same. Ones to the left become zero. Ex: 6185 becomes 6100.
I hope this helps!
I don't understand this question can someone help me with this please, please explain!! and thank you for the help!! If u dont know try your best. Please do it quick :D
Answer:
No, it is not a prime factorization, this is the real prime factorization
Step-by-step explanation:
2⁵x 3 x 5⁴ x 11
The first one was not a prime factorization because 8 is not a prime number.
What is countercurrent multiplication?.
Answer:
What is countercurrent multiplication? ... Countercurrent multiplication in the kidneys is the process of using energy to generate an osmotic gradient that enables you to reabsorb water from the tubular fluid and produce concentrated urine.
For his car, Benny paid $70.96 on speakers and $83.52 on new tires with
wo $100 bills. How much did Benny get in change?
Answer:
If he pays with 2 Hundred Dollar Bills he will get $45.52 in change.
Explanation:
$70.96 + $83.52 = $154.48
2 Hundred Dollar Bills = $200.00
$200.00 - $154.48
please help what is #4?
To Prove:-
JK=IJ
JK= ½IK = IJ= ½IK
JK= IJ(Equal Distance)
GK//HI (Parallel)
Therefore, JK congruent IJ
Hope This Helps
What is the exponential form of the logarithmic equation?
4=log0.7(0.2401)
The exponential form of the logarithmic equation 4 = [tex]log_{0.7} (0.2401)[/tex] is
0.7⁴ = 0.2401
4 = [tex]log_{0.7} (0.2401)[/tex]
The exponential form of the logarithmic equation can be represented below:
Using logarithm rules,
logₐ b = x
Can be represented in exponential form as follows:
aˣ = b
Therefore,
4 = [tex]log_{0.7} (0.2401)[/tex]
using the logarithm rule described above can be represented in exponential form as follows:
0.7⁴ = 0.2401
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Answer:
0.7⁴ = 0.2401
Step-by-step explanation:
A line with a slope of -6 passes through the point (-8, -3). What is its equation in point-
slope form?
Use the specified point in your equation. Write your answer using integers, proper fractions,
and improper fractions. Simplify all fractions.
Answer:
y+3=-6(x+8)
Step-by-step explanation:
Because we already know a point and the slope, we can put our equation in the form y-y1=m(x-x1);
y+3=-6(x+8)
Three-fourths divided by 2 is?
Answer: i think 1/4
Step-by-step explanation: maybe i might be incorrect
Answer:
3/4 or 1 1/2
This is an easy mutiplixation problem
you just turn the 2 into a fraction.
A countertop is 13 feet long and 2 feet wide.
What is the area of the countertop in square meters? Use the conversion 1 foot = 0.305 meter. Round your final answer to 2 decimal places.
Answer:
A = 2.42 sq. meters
Step-by-step explanation:
13 feet = 13 × 0.305 = 3.965 meter
2 feet = 2 × 0.305 = 0.61 meter
A = lw
A = (3.965) × (0.61)
A = 2.41865 sq. meters
A = 2.42 sq. meters
what is the formula for calculating midpoint
The intersection of a line segment's two endpoints is known as the midpoint. From the midpoint to one endpoint and the midpoint to the other endpoint, you will be given two equal distances.
The formula for calculating the midpoint is given below:
[tex] \boxed{ \bold{ \: \: M = \bigg(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\bigg) \: \: }}[/tex]For example, let us try solving this sample problem below using the midpoint formula:
Sample problem: A new transmission tower will be put up midway between two existing towers. On a map drawn on a coordinate plane, the coordinates of first existing tower are (-5, -3) and the coordinates of the second existing tower are (9, 13). What are the coordinates of the point where the new tower will be placed?
From inspection on the given problem:
[tex]\sf (x_1, y_1) = (-5, -3) [/tex][tex]\sf (x_2, y_2) = (9, 13) [/tex]Substitute the given values into the midpoint formula and solve for M:
[tex]\sf M = \bigg(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\bigg)[/tex][tex]\sf M = \bigg(\dfrac{-5 + 9}{2}, \dfrac{-3 + 13}{2}\bigg)[/tex][tex]\sf M = \bigg(\dfrac{4}{2}, \dfrac{10}{2}\bigg)[/tex][tex]\sf M = (2, 5)[/tex]Therefore, the coordinates of the point are (2, 5).
[tex]\\[/tex]
Now, wasn't that easy? Try this other sample problem:
The endpoints of a segment are (-5, 2) and (9, 12), respectively. What are the coordinates of its midpoint?From the sample problem above, you may solve it on your own to enhance your skill on calculating the midpoint.
Cheers!
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
Answer:
D i think sorry if wrong
Step-by-step explanation:
4) Monica swam 4 laps in 15 minutes. At this rate, how many laps would she swim in 45 minutes?
O 8 laps
O 12 laps
O 15 laps
o 21 laps
Answer:
12 laps
Step-by-step explanation:
15÷4=3.75
45÷12=3.75
not sure whether it's true or not but at least I got the answer-
2. Find the value of x. Give your answer in
simplest radical form.
20
16
Answer:
12
Step-by-step explanation:
The Pythagorean theorem shows that 400 or 20² - 256 or 16² = 144 or 12² which means that the other side is 12
x=12
Line A is represented by the following equation: x + y = 2
What is most likely the equation for line B so the set of equations has no solution?
Step-by-step explanation:
Line A : x + y = 2
The most likely equation for line B so that the set of equation has no solution is:
x + y = 4
====
x + y = 2
x = 2 - y
2-y + y = 4
0 = 4 - 2
0 ≠ 2
there is no value for x nor y. so, no solution.
i need help with this
Answer:
88
Step-by-step explanation:
The triangles are congruent. Also, a triangle has a sum of 180 degrees for its interior angles.
Angles D and A are both unknown.
Angles O and P are both 55.
Angles G and W are both 37.
37+55 = 92
That means there would be 88 degrees left for the unknown angle to get to the total of 180 degrees.
92 + 88 = 180